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PAGES 35 AND 102 MISSING FROM ORIGINAL
THE ATTRITIOUS AND FRACTURE
WEAR OF GRINDING WHEELS
by
STEPHEN MALKIN
S.B., Massachusetts Institute of Technology
(1963)
S.M., Massachusetts Institute of Technology
(1965)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF
DOCTOR OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February, 1968
Signature of Author
. . .
M
,Deetment
g/
Certified by..
. ....
,
/
/r-
it
. .
.
F
. .
uary
. .
1, 1968
'.
Thesis Supervisor
Accepted by .
.
.
. .
.
.
Chairman, A partmental Committee on Graduate Students
Archives
Ar
S
ABSTRACT
THE ATTRITIOUS
AND FRACTURE
WEAR OF GRINDING WHEELS
by Stephen Malkin
Submitted to the Department of Mechanical Engineering
February 1968, in partial fulfillment of the requirements
the degree of Doctor of Science
for
A detailed investigation is made of the nature and extent-of grinding wheel wear in finish grinding.
The wear is broadly
either attritious or fracture wear.
classified as
Attritious wear results in the dull-
ing of the tips of the abrasive grain by rubbing against the workpiece
surface. Fracture wear is the removal of abrasive particles from the
wheel either by fracturing within the grain (grain fracture) or fracturing
at the bond
(bond fracture).
Most of the wear is found to consist of
grain and bond fracture particles.
The rate at which fracture wear occurs
is directly related to the grinding
forces.
The attritious wear, although contributing insignificantly to the
total, is the most important
form of wear.
The dulling of the grains by
attrition, measured by the area of the wear flats, uniquely determines the
grinding forces for a particular workpiece material and for given grinding
conditions. Both the horizontal and vertical grinding force components
(For steel this is true only
increase linearly with the wear flat area.
This linear variaup to a critical wear flat area where burning occurs.)
tion between grinding force and wear flat area is explained by considering
the force as the sum of a cutting force due to chip formation and a sliding
force due to rubbing between the wear flats and the workpiece.
Related investigations are also made of wheel dressing, surface finish,
workpiece burn, and grinding temperatures.
Thesis Supervisor:
Nathan H. Cook
Professor of Mechanical Engineering
-ii-
ACKNOWLEDGEMENTS
The author welcomes
Professor
this opportunity
to express his gratitude
to
N. H. Cook for his supervision of this thesis and his
continual interest and encouragement.
He is also indebted to the
members of his thesis committee, Professor
E. Rabinowicz
and Professor
R. L. Coble, for their helpful advice and discussions.
The author gratefully acknowledges
the financial support of
Norton Company, Thanks are due in particular
to Dr. G
S. Reichenbach
of Norton Company, formerly of M.I.T., who supervised
this thesis in
its early stages and continued to be helpful
for the duration of the
work.
A special note of thanks is due to Messrs.
J. Leach, F. Anderson,
and R. Whittemore
S. Marcolongo,
for their
R. Bowley,
practical assistance
in the experimental program.
The facilities of the Harvard University
Computing Center were used
for making numerical calculations. The author's wife, Judithwho is a
member of that organization,
was especially
helpful.
Thanks are also due to Miss Angela Theodore who did the typing.
Finally the author would like to again thank his wife for her
support and assistance.
-iii-
Table of Contents
Title Pag e ..........................................
eeeeeeeeeeeleeel
.
Abstract
..
..
..
..
..
..
..
.
eeeeeleleeeeeeee
............................................
*
AcknowledIgements.....................................
.
.
.
.
.
.
.
.
.
.
.
.
.
6
.....
iii
.0........
iv
'Table of Contents....................................
eeeeeeeeeeeeeeee
eeeeeemeeeeeeeee
vii
xi
List of
Fables ................................................
eeeereeeeeeeeeee
List of
Symbols.....................................
eeeeeeeeeeeeeeee
I.
Intrroduction.
II.
Lite eratureReview
xii
................................... eeeeeeeeeee·eeee
1
of Grinding Wheel Wear........ eeaeeeeeeeeeeeee
4
*
.
0
.
0
.
.
.
.
.
.
0
*
III. Equi.pment,Material, Procedures, and Parameters.eeeeeeeeeeeeeeee
3.1. Introduction .............................
3.2. Equipment.....................
3.4. Workpiece Materials
13
........ eeeeeeeee:eeeeeee
13
eeeeeeeeeeeeeeee
....................
3.5. Parameters .............................
0
.
0
0
0
.
.
.
0
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17
eeeeeeeeeeeeeeee
*
v
v
.v
.v
.
0
0
.
.
Forces and Energy ...... leeeeeleeeeeeeee
3.5.2. Per Cent Wear Flat Area .........
18
eeeeeeeeeeeeeeee
..
..
.
0.....
...
3.5.3. Active Grains per Unit Area..... eeeeeeeeoeeeleel
0.
.0..
..
0...
0.
3.5.5. Per Cent Bond Fracture..........
...
21
0......
eeeeeeeeeeeeeeee
..
0.
.
.
..
0.
.
.
.
.
.
.
0
.
0
.
.
.
.
25
11
-
4.1. Introduction...........................eeeee~eeeeeoeeee
4.2. Results ...
..
,
.
.
0..
*
0
.0..0..
4.3. Discussion...........................
-iv-
25
.0..
................
..
eeeeeeeeeeeeeeee
.
.
0
.
.
.
22
.....
eeeleeeeeeeeeeee
Dres3sing.......................................
*
20
......
3.5.4. Grinding Wheel Wear............. eeeleeeeeleeeeee
..
17
.0..0......-
......
..
16
16
eeeeeeeeeeeeeeee
*
3.5.1. Grinding
13
eeeeeeeeeeeeeeee
3.3. Grinding Wheels .*................... ...
IV.
ii
.
eeeleeeeeeeeeeee
List of FFigures......................................
i
eeeeeeeeeeleeeee
.
.
0
.
.
26
.
32
V.
Attritious
Wear and (Grinding Forces.......
............
36
5.1. Introductiorn.....................
eeeeeeeleee.
36
.~eeeeeeeee,
36
..........
*
.
.
.
.
.
.
.
.
.
... eeeeee.
5.2. Results....
.........
5.3. Discussion.,
.. e...................
53
...........
ee........
VI.
Grinding Temperaturesn.....................
66
.. eeeeeeee
6.1. Introductioi ...........eeeeee..ee,
* .
.
.
66
.
. .
.
.
.eeeeeeee·ee
eeeeeeeeeeee
.
6.2. Geometry of Chip Formation.......
eoe·eeeeeeee
67
6.3. Energy Partdition .................
eee·eee·eee.
71
6.4. Calculated (Grinding Temperatures.
.eeeee·eeeee
74
1...................
VII. Surface Finish........
79
...........
.e..e....
.eeeeeeeeeee.
eeeeeeeeeee.
7.1. IntroductiorI.....................
.
.
.
.
.
.
.
.
..
.
.
7.2. Results and Discussion...........
rVIII.Fracture Wear
.....
..
.
.
79
.eeeeeeeeeee
79
.
.
.
.
.
eeeeee·leee.
8.1. Introductior
eeeeee·eeeee
82
82
..........
8.2. Results....
eeeeeeeeeeee
82
.eeeeeeeeeee
91
.eeeeee·eee.
96
..........
8.3. Discussion.
*
IX.
Conclusions .........
X.
Suggestions
e
*
ee
e
e
.e
!Gr
..eeeeeeeeee
for Futuire Work..............
References...............
.....
Grains
eeeeeee·eeeee
.......
Appendix A.
Calculation 4of the Maximum Number of Active
Appendix B.
Calculation 4of Temperatures
due to
Appendix
C.
Calculation
of Temperatures
due to Sliding. *............
Appendix D.
Calculation
of the Average Temperature
Cutting.
..
,............
,.eeeeeeeeee.
@*
99
101
105
106
108
in the
Grinding Area......................................... 110
Tables.............................
........
Biographical Notee......................................
-vi-
......... 111
131
List of Figures
No.
Title
1.
Illustration
2.
Photograph of the equipment ..................................
3.
Microphotograph
4.
Number of active grains/inch2 versus bond per cent
Page
of the three types of wear ..............................
3
of wear flats
.......................................
19
for fine and coarse dressing
...............................
5.
............................ 28
Wear flat area per grain versus bond per cent for
fine and coaxse dressing ................................
7.
Number of active grains per square inch versus 100 minus
for dressing particles
...............
34
Grinding forces and force ratio versus number of passes
for 1018 steel workpiece,
v
11.
... 30
...................................... 31
per cent bond fracture
10.
......
Per cent bond fracture versus bond per cent for dressing
particles....
9.
29
Particle size distribution for dressing particles
and
abrasive
grain.... .. .... .
8.
27
Wear flat area versus bond per cent for fine and
coarse dressing............
6.
14
8 ft./min.,
d
fine dress, V
6250 ft,./min.,
.001 in ..................................
37
Per cent wear flat area and wear flat area per grain
versus number of passes for 1018 steel workpiece,
dress, V = 6250 ft./min., v - 8 ft./min., d
-vii-
fine
.001 in ........
38
12.
Grinding forces and force ratio versus number of passes
for 1018 steel workpiece,
coarse dress, V = 6250 ft./min.,
................................
39
v = 8 ft./min., d = .001 in ..
13.
Per cent wear flat area and wear flat area per grain
versus number of passes for 1018 steel workpiece, coarse
dress, V = 6250 ft./min., v = 8 ft./min., d = .001 in ..........
14.
Number of active grains/inch
1018 steel workpiece,
d
15.
= .001 in
Microphotographs
V
2
versus bond per cent for
6250 ft./min., v = 8 ft./min.,
......................
...............
........
.......
41
of wear flats after 20, 40, 60, 80, and
..................
100 passes ...............................
16.
40
43
Grinding forces versus wear flat area for 1018 steel,
fine and coarse dress, V = 6250 ft./min., v = 8 ft./min.,
d = .001 in
17.
.
..................................................
45
Grinding forces versus wear flat area for 52100 steel,
fine dress, V = 6250 ft./min., v
.18.
-
6250 ft./min., v = 8 ft./min.,
Grinding
Grinding
d = .001 in .................. 47
=
8 ft./min., d = .001 in .....
48
forces verses wear flat area for niobium, fine dress,
V = 6250 ft./min., v - 8 ft./min., d = .001 in ................
21.
46
forces versus wear flat area for 130 A titanium,
fine dress, V = 6250 ft./min., v
20.
8 ft./min., d = .001 in .....
Grinding forces versus wear flat area for T1 steel, fine dress,
V
19.
-
Grinding forces versus wear flat area
for molybdenum,
fine dress
V = 6250 ft./min., v = 8 ft./min., d = .001 in ...............
-viii-
49
50
22.
Grinding
forces versus wear flat area, for Stellite
fine dress, V = 6250 ft./min., v
23.
Grinding
8 ft./min, d = .001 in.....
51
forces versus wear flat area for 1018 steel,
fine dress, V = 3125 ft./min., v
24.
No. 6B,
Illustration
of chip formation
sliding force components
4 ft./min., d = .001 in....
=
and the cutting and
......
.....
...
.........................
54
25.
Illustration of the grinding geometry.........................
26.
Pressure distribution due to contact between a punch
and a semi-infinite
elastic solid
Specific cutting energy versus wear flat pressure .
28.
Specific cutting energy versus melting
point of the workpiece..
.29.
Geometry
.....
:30.
Geometry of chip formation.
31.
Fraction of grinding
chip ...
56
.............................
59
27.
of undeformed
52
.
............62
...
63
.........................
68
...................................
72
energy conducted
to the workpiece
versus
the wear flat area for 1018 steel, fine dress, V = 6250 ft./min.,
v = 8 ft./min.,
32.
d = .001 in ...............................
73
Variation of thermal conductivity and thermal diffusivity
with temperature for mild steel .............................. 75
33.
Distribution
of calculated grinding
workpiece
surface........................
34.
temperatures along
...
. ....... .....
77
Surface finish versus the number of passes for fine and
coarse dressing for 1018 steel, V
v = 8 ft./min.,
=
6250 ft./min.,
d = .001 in ...................................
-ix-
80
35.
Accumulated
wear versus number of passes for 1018 steel,
6250 ft./min., v = 8 ft./min., d
fine dress, V
36.
Accumulated wear versus number of passes for 1018 steel,
coarse dress, V - 6250 ft./min., v
37.
Accumulated
8 ft./min., d - .001 in....
84
wear versus number of passes for 52100 steel,
fine dress, V
38.
.001 in ...... 83
6250 ft./min., v
8 ft./min., d
.001 in ...... 85
Particle size distribution of wear particles and abrasive
grain for 1018 steel, fine dress, V - 6250 ft./min.,
v
39.
8 ft./min., d
.001
in .....................................
87
Particle size distribution of wear particles and abrasive
grain for 1018 steel, coarse dress, V - 6250 ft./min.,
v
40.
8 ft./min., d - .001
in ..................
,.....................
88
Particle size distribution of wear particles and abrasive
grain for 52100 steel,fine dress, V
v - 8 ft./min., d
.001 in .... ..
6250 ft./min.,
...
.....
..
..
89
41.
Per cent bond fracture versus bond per cent for wear particles.. g90
42.
Illustration
43.
Correlation between the wear per active grain and the
of the force on an active grain ....................
bond stress factor
.....
92
...........................................
95
List of Tables
No.
Title
1.
Description
2.
Workpiece Materials..........................
3.
Wheel Dressing - Experimental Results..........
4.
Sieve Number - Screen Opening............................. 114
5.
Forces and Wear Flats - 1018 Steel, Fine Dress.............
115
6.
Forces
and Wear Flats - 1018 Steel, Coarse Dress ..........
116
7.
Forces
and Wear Flats - 52100 Steel, Fine Dress ...........
i17
8.
Forces
118
and Wear Flats - T1 Steel, Fine Dress.................
9.
Forces
and Wear Flats - 130 A Titanium, Fine Dress.........
119
10.
Forces
and Wear Flats - Niobium,
120
11.
Forces
and Wear Flats - Molybdenum, Fine Dress.............
121
12.
Forces
and Wear Flats - Stellite No. 6B, Fine Dress........
122
13.
Forces and Wear Flats - 1018 Steel, Fine Dress .............
14.
Summary of Results Frc)m Least Square Analysis.............. 124
15.
Energy Partition - 10118 Steel, Fine Dress ..................
125
16.
Surface Finish, 1018 Steel................
12(
17.
Wheel Wear - 1018 Steel, Fine Dress.......
127
18.
Wheel Wear - 1018 Steel, Coarse Dress.....
128
19.
Wheel Wear - 52100 Steel, Fine Dress......
129
B.1.
Calculated
130
Page
of Whee6s
.........................
-xi-
.
.
.0
..
.
.
111
.
.
.
..
..
.
.
112
Fine Dress................
Values of T ...................
c
.
00000000000000000
.................
113
123
LIST OF SYMBOLS
Symbol
Description
Dimensions
a
Semi-width of punch
in.
aA
Apparent
in. 2
area of contact
between wheel and workpiece
aR
Real area of contact between
wear flats and workpiece
in.2
A
Wear flat area
per cent
lb
Width of cut
in.
Per cent of wear due to bond
per cent
iB
fracture
c
Correlation coefficient
C1
Constant
C2
Constant
C
Number of cutting points per
unit area
in -2
d
Downfeed per pass
in.
D
Wheel diameter
in.
f
Function used for contact
pressure distribution
fH
Horizontal
fV
Vertical
FH
Horizontal grinding force
FHC
Horizontal
force per grain
force per grain
force due to cutting
-xii-
lb.
lb.
lb.
lb.
Description
FHS
Horizontal
Fv
Vertical force
lb.
Vertical
force due to cutting
lb.
Vertical
force due to sliding
lb.
FVC
FVS
force due to sliding
Dimensions
H
Workpiece hardness
I
Function used for moving heat
source calculation
k
Thermal conductivity
K
Constant
,1
Semi-width of band for moving
heat source calculation
1C
Undeformed chip length
L
Nondimensional variable in
moving heat source calculation
m
Number of grains per unit weight
lb.
lb./in.2
lb./sec.
OF
of abrasive
M
Number of whole grains corresponding
to a given weight of abrasive
11
Number of active grains "instantaneoudly"
in contact with workpiece
N
Number of contacts which occur
between active grains and workpiece
p
Contact pressure between punch
elastic solid or between wear flat
and workpiece
lb
p
Average contact pressure between
wear flats and workpiece
lb.
-xiii-
/in.2
/in.2
Symbol
Description
Dimensions
Probability that a grain will
experience a bond fracture for
each contact between a grain and
the workpiece
P
Force per unit width between
punch and semi-finite solid
q
Grinding energy flux
qf
Energy flux due to sliding
between wear flats and workpiece
Q
Total grinding power
r
Ratio of width
lb./in.
2
in. lb./in.
in. lb./in.
in. lb./sec.
to thickness
of undeformed chip
R
Fraction of grinding energy
conducted to workpiece
Fraction of cutting energy
conducted to workpiece
Fraction of sliding energy
conducted to workpiece
tl
Undeformed chip thickness
in.
(tl)max
Maximum undeformed chip
thickness
in.
t2
Actual chip thickness
in.
Actual chip thickness when
in.
the cut is 50% complete
(t 2 )max
Maximum value of t2
TA
Calculated temperature
rise over the grinding area
-xiv-
in.
sec
Symbol
(TA)ave
(TA)max
Dimensions
Description
Average value of TA
Maximum value of TA
TC
Calculated temperature rise
due to cutting
(Tc)ave
Average value of TC at
(TC)max
Maximum value of T
shear zone
u
Specific grinding energy
in. lb./in. 3
u
Specific cutting energy
in. lb./in. 3
v
Velocity of workpiece
ft./min.
VII
Velocity of wheel periphery
ft./min.
Velocity of moving heat
source
ft./min.
Vb
shear zone
at
Fraction by weight of bonding
agent in the wheel
w
Wear per "instantaneous" active
mg.
grain in 20 passes.
W
Wear in 20 passes
mg.
x
Coordinate of punch; wear
flat, and moving heat source
in.
X
Nondimensional coordinate of
moving heat source
oi
Thermal diffusivity
2
in. /sec.
Constant
A?
Shear angle
-xv-
degrees
I.
INTRODUCTION
Grinding of metals is similar to other metal
cutting operations
as metal is removed by a shearing process of chip formation.
cutting operations
a tool of known geometry and orientation
grinding is accomplished by numerous
insofar
In most metal
is used, but
tools (abrasive grains) of varied and
indeterminate geometry. These hard abrasive grains are held together by a
weaker bond to form a grinding wheel.
As the wheel rotates, the grains cut
chips out of the workpiece.
As a grinding wheel wears,
the surface of the wheel becomes uneven.
Dulling of the abrasive grains also occurs.
in the quality of the workpiece
surface.
This leads to deterioration
For finish grinding where precise
surfaces of low surface roughness are required, it is necessary to periodi-
cally sharpen or dress the wheel.
For abrasive machining, where the objective
is bulk metal removal, the quality of the surface is relatively unimportant
and the grinding wheel is not periodically
dressed.
The present investiga-
tion is concerned only with finish grinding.
The main difficulty
encountered by the grinding
of the grinding wheel best-suited
for a given work.
engineer is the choice
It is often found that
the best grinding wheel for the job is the one which experiences
wheel wear.
the least
This is not due to the cost of the wheels because in finish
grinding that cost is but a small portion of the total expense.
The general
belief is that if the wheel consumption
time required
is low, the unproductive
for dressing the wheel will be less and the grinding operation will be more
efficient.
-1-
It is therefore not surprising
that grinding wheel wear has been
the subject of numerous investigations.
Most of these investigations
are empirical in nature and the experimental
cable only to the particular
been a pitiful
results are usually appli-
case at hand or a similar one.
There has
lack of basic research in this area.
Grinding wheel wear can be broadly classified as either attritious
wear or fracture wear.
Attritious wear results in the flattening or dull-
ing of the abrasive grain by rubbing against the workpiece surface, illustrated by (A) in Figure 1.
grinding wheel.
This accounts for the glazed appearance of a
Fracture wear is the removal of abrasive particles from
the wheel by either fracturing within
the grain (grain fracture), illus-
trated by (B) in Figure 1, or fracturing
at the bond (bond fracture),
illustrated by (C) in Figure 1.
This thesis describes a detailed investigation into the nature and
extent of grinding wheel wear.
The total wear is measured
of the grinding wheel wear particles.
statistical
The wear particles are sieved and a
analysis is used to determine
the relative amounts of grain
fracture, bond fracture, and attritious wear.
measured
from the weight
The attritious wear is also
as the area of the wear flats generated on the grains.
ficance of these different
The signi-
types of wear is clearly observed.
Related investigations are also made of grinding forces, wheel dressing, surface finish, grinding
temperatures,
-2-
and workpiece burn.
Figure 1.
Illustration of the three types of wear.
A - attritious wear, B - grain fracture,
C - bond fracture.
-3-
II.
LITERATURE REVIEW OF GRINDING WHEEL WEAR
The first significant scientific investigation of the grinding process
was performed by G.I. Alden of the Worcester
Polytechnic
Institute.
report "Operation of Grinding Wheels in Machine Grinding" (
the A.S.M.E. in 1914, a mathematical
)
In his
presented to
relationship was derived for the "grain
depth of cut" or chip thickness as a function of the grinding conditions.
Alden reasoned that the wear of the grinding wheel "on a given kind of work
is almost entirely dependent upon the grain depth of cut", a larger depth of
cut causing greater wear.
Almost twenty years later, a Swedish engineer, R. Woxen, working
country at Norton Company, performed
in this
the first extensive and systematic
inves-
tigation of grinding wheel wear.(2) W6xen introduced the wheel wear parameter
which he called the specific wear, which is defined as the volume ratio of
wheel wear to metal removal.
index or G-ratio
(grinding ratio) which
describe grinding wheel wear.
wheel
This is equal to the inverse of the grindability
is almost exclusively used today to
He also originated the notion of a grinding
tool life which is arbitrarily
judged from the deterioration
of the
workpiece surface.
The specific wear and the grinding wheel life were related to the grinding variables
(wheel speed, table speed, chip thickness, metal
removal rate)
from which the optimum grinding conditions could be determined. He concluded
that the specific wear "is not univocally
chip-thickness as Alden supposed".
-4-
(unequivocally) determined by the
At this point a question of semantics
of grinding wheel wear.
The G-ratio
arises over the definition
is in fact a measure of the efficiency
of the grinding operation where the objective is maximum metal removal with
minimum wheel wear.
In finish grinding, which is considered here, the abra-
sive cost usually represents
an insignificant
expense of the grinding operation.
contribution
to the overall
In fact, more abrasive is used in dress-
ing the wheel than during grinding.
This was clearly recognized by both
Alden and Woxen.
From an analytical point of view, it is probably better to consider
wheel wear as the weight
(or volume) of abrasive removed for a given length
of travel of the wheel periphery.
This is consistent with conventional
practice in the general treatment of other wear systems.( 3 )
Alden may
have thought of wear in this way, in which case, his belief that grinding
wheel wear is determined from the grain
depth of cut has never been really
explored.
Most experimental studies of grinding wheel wear consist of measuring
the G-ratio and the specific energy
particular
set of grinding
(power consumed/metal
conditions.
limited success in optimization
removed) for a
While this approach has enjoyed
of grinding conditions, very little has been
learned about the fundamental aspects of grinding wheel wear.
small changes in grinding conditions
differences
Tarasov
steels.
Furthermore,
often lead to large unexplainable
in the G-ratio.
(4)
used this approach to investigate
the grindability of tool
He concluded that "the power or energy consumed in grinding cannot
-5-
be used to predict the grindability
(G-ratio) of tool steels, since these
can be the same for steels known to be extremely difficult to
quantities
grind as for those comparatively easy to grind."
obtain some correlations between
On the other hand, he did
the alloy content of the steel and its
G-ratio.
Essentially the same approach was taken by Backer and Merchant(5 ) who
measured
the G-ratio, grinding
forces, and specific energies for several
grades of aluminum oxide wheels on steel and cast iron.
Attempts
to corre-
late the G-ratio with specific energy, chip area, chip length, and cutting-
speed were unsuccessful.
For mechanisms of grinding wheel wear have been proposed by Peklenik(6' 7 )
1.
Pressure softening of the grain due to high temperature producing
wear flats
of individual
crystals from the grain
2.
Splintering
3.
Partial grain dislodgement
4.
Complete grain dislodgement
The first of these is dulling of the grain.
The second and third are types
of grain fracture, and the fourth is bond fracture.
Peklenik
considered
the wear flats in grinding
flank wear of a cutting tool.
to be analogous to the
The dulling of the grains was quantitatively
expressed by the fraction of the total active area of the grinding wheel on
which wear flats appear. This was measured by running carbon paper between
the grinding wheel and a piece of glass.
A replica of the wear flats is
transferred to the glass as black carbon spots. The wear flat area is
-6-
determined with a planimeter
from an enlarged photograph of the glass.
The tests showed that when a given wear flat area was reached, burning of the steel workpiece occurred.
This critical wear flat area was
found to be between 5 and 10 per cent, the larger wear flat area corresponding
to wheels of smaller grain size.
was proposed'as
Therefore the wear flat area
a criterion of grinding wheel tool life ("Verschleisskri-
terium").
Yoshikawa(8' 9) arrived at essentially the same conclusion. In his
tests the wear flat area was determined
wheel taken through a microscope.
from photographs
of the grinding
With the proper lighting,
the wear
flats exhibit a mirror-like effect and stand out brightly over the dark
background
of the rest of the wheel.
corresponding
their weight
The white traces in the photographs
to the wear flats were cut out and weighed.
to the weight of the original photograph
The ratio of
determined
the wear
flat area per cent.
At a critical wear flat area of 8 per cent, a sharp rise in the grinding forces occurred.
For smaller wear flat areas, the grinding forces were
found to be essentially
results presented
constant.
(This last observation
is contrary to
in this thesis and will be discussed in detail.)
He
concluded that the grinding life depends on an increase of wear flat area
due to attrition and a decrease of wear flat area due to fracture.
Tsuwa( 1 0 , 11) investigated
observing
the progress of individual wear flats by
the profile of the grain tips.
wear flats were measured.
Both the breadth
and number of
The changing nature of the cutting edges were
-7-
attributed to
1. Attritious wear
2.
Grain breakage
3.
Dig out (bond fracture)
4.
Newly appeared grains
The first and fourth increase the wear flat area, the second and third
decrease it.
A photoelectric device was also developed to automatically determine the number
and area of wear flats on the wheel.(11) The number of
wear flats was determined
from the number of light peaks reflected from
the duration of the light peaks.
Tsuwa et al (1 2 ' 13) made numerous detailed
flat surfaces.
of the wear
Wear flats were found to develop on the vitreous bond as
well on the grain.
mately
bservations
The ratio of bond to grain wear flat areas was approxi-
equal to the relative amounts of bond and grain in the wheel.
Two types of surfaces were observed on the worn grain.
smooth and has striations
parallel to the grinding direction.
contains a network of cracks, and is quite rough.
only the first region appears.
The first is
The other
At the beginning of wear
As the wear flat grows, the second region
suddenly appears at the trailing edge, presumably where the temperature
is
greatest.
Attritious wear was also measured by Iahn(1 4
and Lindsay(15) for con-
trolled force (constant normal force) internal grinding.
Wear flat areas
were determined from planimeter measurements on microphotographs of the
-8-
wheel surface.
As grinding proceeded,
was accompanied by a proportional
It was also reported
the increasing wear flat area
decrease in the metal removal rate.
(16) that the natural roughness of the wear flat
surface corresponded to the best surface finish obtainable on the workpiece.
The dressing
technique can have a strong influence on the size of
the wear flats observed.
Lind-say( 15
)
ing technique (higher infeed velocity
found that when a coarser dressof dressing tool) was used, less
wear flat area was observed on the wheel.
A finer dressing technique
was believed to dress a larger initial wear flat area on the wheel.
I1
D.K. Bruckner
(17)
showed that increasing wear flat areas were
accompanied by increased radial wheel wear.
was used for the wear flat measurements.
Peklenik's pocedure
For low alloy and structural
steels, the radial wheel wear before redressing
one-tenth of a grain dimension.
plete grain dislodgement
(7 )
amounted to only about
From this it was concluded that com-
(bond fracture) was very unlikely
to be a sig-
nificant form of grinding wheel wear.
The attritious wear of abrasive
occurs at high temperatures where
chemical interaction
and Williams
(18)
rubbing against the workpiece
the wear rate should depend on the
between the grain and workpiece materials.
investigated
surface
Goepfert
the attritious wear of single point tools
of aluminum oxide and silicon carbide abrasive against various metallic
materials. Qualitative assessment of chemical interaction was independently
obtained from metallographic
observation
of the reacting material pairs
which had been placed in contact and heated.
-9-
In general those combinations
with higher wear rates also had more extensive reaction. These results
the overall wear of grinding wheels.
were not applied to interpreting
In this same paper, the effect of grain toughness on the G-ratio
is also indicated.
Grain toughness is an arbitrary measure of the break-
clown resistance of the material
under impact loading, a high toughness
breakdown
number signifying a low percentage
of particles.
However,
was found to increase with toughness.
The G-ratio
this result is of limited
value since neither the test conditions nor numerical
results are reported.
The general shape of the radial wheel wear curves has been found by
Backer and Krabacher
regimes.
( 19 )
and Grisbrook
et al ( 20 ) to consist of three
In the first regime there is a high initial wear rate which
decreases with time.
This is followed by a more or less constant wear
rate in the second regime and an increasing wear rate in the third regime.
The same type of wear rate curve is often found in other situations,
(e.g.
wear lands on cutting tools, ball bearing wear,) where the three wear
regimes are called run-in, run-with,
Pattinson and Chisholm
( 2 1)
and run-out.
considered
wear in the first and second regimes.
the effect of dressing on the
With coarser dressing technique
(larger
crossfeed velocity of dressing diamond) the initial wear rate of the wheel
is higher.
In the second regime, however,
affected by the dressing
Grisbrook et al (2 0
the wear rate appeared to be un-
technique.
)
stated that the increasing
rate of wheel wear in
the third regime is due to bond fracture, where whole grits are being dislodged from the grinding wheel.
No experimental
support this contention.
-10-
evidence was presented to
(22) attempted to correlate grinding wheel wear with the
Colding
"grinding equivalent", which is the ratio of the length of the chip
to its cross-sectional
area.
The only reasoning which underlies a
possible connection between the wheel wear and grinding equivalent is
that a somewhat analogous
cutting edge length to
chip equivalent
(the ratio of total engaged
the cross-sectional
area of the chip, before
metal removal) was used with some success in correlating
for milling and turning.
Using W6xen's
log-log plot, a linear relationship
the tool life
data, Colding did obtain, on a
between
the G-ratio and the chip
equivalent. Other data did not provide such a neat correlation.
Yoshikawa
wheel wear.
and Sata (2 3 ) took a new approach
to the problem of grind-
They classified the wheel wear as
1.
Attritious wear
2.
Mechanical
3.
Fracture of bond bridges (bond fracture)
fracture of grains
The third type of wear was theoretically
(grain fracture)
considered
from the standpoint
of delayed fracture of brittle materials. Analytical results indicate
that the rate of bond fracture varies
linearly with grinding time and
exponentially with the stress on the bond.
to vary linearly with the resultant
Experimental verification
force per grain.
of the effect of grinding time and force
on the rate of bond fracture was obtained
(F-grade).
The bond stress is assumed
for a weakly bonded wheel
With a soft wheel such as this, the average wheel wear particles
are only slightly smaller than the grains used in the wheel production.
-11-
Virtually
all the wear id due to bond fracture.
In a later paper, Yoshikawa
(2 4 )
attempted
to generalize
this
The overall wear was analyti-
approach for harder grades of wheels.
cally determined as the sum of grain fracture and bond fracture particles.
The predictions were partially
supported by experiments using
grinding wheels of different grades. The complex form of the analytical expressions preclude their practical application.
The theoretical analysis presented
be questioned on several points.
in these last two papers might
However,
it is more important to real-
ize that this approach is the only instance in the literature where an
attempt was made to come to grips with the complex problem of grinding
wheel wear in fundamental terms. A similar approach to the problem is
used in this thesis.
-12-
EQUIPMENT, MATERIAL, PROCEDURE, AND PARAMETERS
III.
3.1
Introduction
Numerous
experimental techniques and parameters have been
devised to characterize the behavior of grinding wheels and the grinding
process.
Yet there are hardly any routine tests or standardized
symbols which have been adopted by the various laboratories engaged in
basic grinding research.
appear
In some instances,
in the literature" where different
apparent contradictions
techniques were used to
measure what was thought to be the same physical value.
Therefore,
it
is especially important in grinding research to closely identify
experimental results with the methods by which they were obtained.
In this section the equipment, materials,
of the parameters used in this investigation
detail.
and some
procedures
are discussed
These are also compared to similar experimental
in some
techniques
used by other investigators.
3.2
Equipment
The experimental
in Figure 2.
apparatus used in this investigation
All the tests were run on a Norton 6 x 18 surface grinder
using 8 inch diameter wheels
(8 inch diameter x 1/2 inch wide and 1 1/4"
bore) on a 1/4 inch wide workpiece
crossfeed).
is shown
under plunge
cut conditions
(no
This machine has a D.C. drive variable speed spindle and
-13-
Figure 2.
Photograph of the equipment. Note the microscope which
can be positioned to view the wear flats and the box for
collecting the wheel wear and chips.
-14-
a variable
speed hydraulic drive table.
Most tests were run at a wheel
speed V = 6250 ft/min. with a table speed v = 8 ft/min., and a down
feed d
.001 inch.
Both the horizontal and vertical
components of the grinding force
FH and FV were measured with a very stiff and sensitive semiconductor
strain gage dynamometer
Semiconductor
connected to a Sanborn Model 150 recorder.
strain gages are about 50 times more sensitive than the
conventional wire gages.
approximately
This dynamometer
has a stiffness of
700,000 pounds per inch, and thus is about 50 times
more rigid than the grinding machine.
Force differences
as small as
.02 pounds can be detected.
Grinding wheel wear was determined from the weight of wear
particles
generated in a given number of passes.
The wear particles
were collected together with the metal removed and ultimately
separated by chemical means. The particles were then weighed and
sieved.
Details of these procedures
are given below.
With a microscope attached directly to the machine, both the
wear flat area and the number of active grains per unit area were
determined without
removing the wheel
from the spindle.
of the procedures used for these measurements
The details
are discussed below.
Surface finish measurements were made with a Cleveland Roughness
Meter Model BK6101
(not shown in Figure 2).
With this device, a
hand held instrument was traversed along the workpiece surface.
Measurements were taken intermittently without removing the workpiece
from the dynamometer.
The results, indicated on a meter, were
-15-
estimated
to 1 microinch A.A.
finish of 20 microinches
(arithmetic average) below a surface
A.A. and to 5 microinches
A.A. with coarser
finishes. Although there were more refined instruments available for
obtaining
finer surface finish measurements,
instrument was
3.3
more than sufficient
the accuracy of this
For this investigatfon.
Grinding Wheels
The grinding wheels furnished by Norton Company for this
investigation
are described
in Table 1.
These wheels vary only in
grade which is determined by the amount of vitreous bonding material
in the wheel.
The abrasive is
!o:rton's32 Alundum
(32 A), a light
gray colored single crystal aluminum oxide of high purity which is
widely used for grinding steel.
mean grain diameter of about
3.4
The 46 grain size corresponds
to a
.015 inch.
Workpiece Materials
The workpiece materials are listed in Table 2 together with
their chemical composition and room temperature hardness.
materials were used for the attritious wear studies.
Only the 1018
and 52100 steels were used for the fracture wear studies.
were 1/4 inch wide and initially 2 inches high.
All these
The specimens
The 1018 and 52100
steel specimens were 4 inches long, and the other specimens were 2 inches
long.
-16-
3,5
Parameters
3.5.1
Grinding Forces and Energy
As previously mentioned, both the horizontal and vertical components
of the grinding forces, FH and FV, were measured with a semiconductor
strain gage dynamometer.
This instrument was sufficiently stiff so
that it would have had virtually no influence on the grinding process
itself.
In the past, grinding forces have been typically measured with
dynamometers using conventional wire strain gages. To achieve adequate
sensitivity, these devices are rather flexible. For instance, Marshall
and Shaw(2 5 ) report using a dynamometer with a stiffness approximately
equal to that of the machine
itself.
of the grinding system in half.
This in effect cuts the stiffness
Machine
stiffness is a significant
factor in grinding, and there is a concerted effort today to build
very rigid grinding machines.
The grinding force measured by the dynamometer
sum of the forces between
represents the
the active grains and the workpiece.
The
tangential component of the grinding force can be used to compute
the specific grinding energy, u, which is defined as the energy
required to remove a unit volume of material.
widely used in metal cutting research.
For surface grinding with
wheel speeds much greater than table speeds,
FH
multiplied
This parameter is
the horizontal force,
by the wheel velocity, V, is the total power input.
-17-
With a high G-ratio, the metal removal rate is the product of the table
speed, v, the downfeed or wheel depth of cut, d, and the width of cut,
b.
The specific grinding energy is given by the ratio of the power
input to metal removal rate.
FH V
u
3.5.2
=
(3.1)
v bd
Per Cent Wear Flat Area
The attritious wear of the grain rubbing on the workpiece surface
leads to the development and growth of wear flats on the active grains
in the wheel.
The percentage of the total area was measured with a
microscope attached directly to the grinding machine. This microscope
had a self contained illuminator
the objective lens.
with a light coming directly through
When the microscope
was focussed normal to the
wheel surface, the wear flats reflected light directly back through
the microscope.
The remainder of the wheel surface reflected the
light in random directions and appeared quite dark. A photograph
of a typical observation
is shown in Figure 3.
The fraction of the
total viewing area covered with the wear flats was easily estimated
with
the aid of a fine grid on a reticle mounted in the eyepiece.
A minimum
of ten locations chosen at random on the face of the wheel
were used for each measurement.
-18-
35 X
Figure 3.
Microphotograph of wear flats. Wheel - 32A461I8VG,
workpiece - 1018 steel, V = 6250 ft./min., v = 8 ft./min.,
d = .001 in. Taken after 60 passes.
-19-
The main advantage of this technique for wear flat area measurements,
as compared to most of those described previously
in this thesis (see
Literature Review), is its efficienty and simplicity.
other methods,
which to work.
it is not necessary
It is possible
Unlike the
to take numerous photographs
from
to obtain a data point here in a few
minutes where the other methods normally require hours of work, and
the amount of data previously gathered has been rather limited.
3.5.3
Active Grains per Unit Area
There have been numerous attempts to measure the effective number
of cutting points per unit area
of a grinding wheel
parameter
(or their mean spacing) in the surface
ofa grinding
(6,
10, 11,
wheel
14, 15, 21, 23, 24, 26, 27, 28)
This
is usually confused with the number of active grains per unit
area, the number of wear flats per unit area, or some other measurement
which is related to a particular
experimental
procedure.
The tacit
assumptions are that there can be only one cutting point per grain, one
wear flat per grain, and one cutting point per wear flat.
these assumptions
None of
are justified.
In the present investigation,
the number of active grains per
unit area in the surface of the grinding wheel is a particularly
important parameter.
To illustrate,
it is used together with the
grinding force and wear flat measurements for the calculation of
the average grinding force and wear
flat area per active grain.
-20-
The number of active grains was experimentally determined with
the microscope together with the wear flat measurements previously
described.
By lighting the wheel surface at a glancing angle, still
viewing normal
to the surface, the grain corresponding
wear flat could be seen.
to a particular
The total number of grains on which
there
were wear flats divided by the viewing area was the number of active
grains per unit area.
Numerical
results obtained in this manner
were typically lower, by a factor of two or more, than measurements
reported by other researchera on similar grinding wheels. This was,
of course, to be expected.
A single grain may have more than one
wear flat and more than one cutting point.
3.5.4
Grinding Wheel Wear
Grinding wheel wear is usually expressed by the G-ratio, which
is defined as the volume ratio of metal removed to wheel worn.
volume of wheel worn
The
is given by the product of the decrease in
wheel radius, the circumference
wheel used for grinding.
of the wheel, and the width of the
The actual measurement
of the decrease of
wheel radius is usually made with a micrometer.
For finish grinding,
the radial wheel wear before redressing
typically amounts to about one-tenth of a grain dimension.
be shown that most of the wear
(by weight)
It will
consists of particles
which are almost as large as the initial grains.
Therefore most of
the wear consists of particles whose average diameter is much larger
-21-
than the decrease in wheel radius, and the measurement
of the wear
in this way does not give a true indication of the amount of abrasive
removed from the wheel.
This would account, at least in part, for
the lack of success in correlating
the radial wheel wear
(or G-ratio)
with other parameters of the grinding operation.
In this thesis, the overall grinding wheel wear was determined
from the weight of grinding wheel wear particles. A special box-like
collector described above was constructed which enabled virtually all
(See Figure 2)
the wear debris to be collected.
The interior of
this container was coated with white petrolatum grease which caught
the debris as it was generated.
The wheel wear particles were
ultimately separated by dissolving away the grease in boiling
trichlorethylene
and the chips in aqua regia acid solution which does
not attack aluminum oxide. Wheel wear particles were sieved and
weighed on an electric balance to determine
the total wear and particle
size distribution.
3.5.5.
Per Cent Bond Fracture
Grinding wheel wear particles
are generated
the grain at the bond, fracture within
grain on the workpiece
surface.
as bond fracture, grain fracture,
from the fracture of
the grain, and rubbing of the
These are'respectively
and attrition.
referred to
Bond fracture wear
particles are almost as large as the grains used in the wheel
manufacture.
Grain fracture particles are somewhat smaller, about
-22-
half as large as the grains.
Attritious
wear particles are orders
of magnitude smaller. Experimentally, most of the grinding wheel
wear is found to consist of particles
almost as large as the initial
grains, and only about five per cent of the wear consists of particles
small enough to be caused by attrition.
In other words, about ninety-
five per cent of the total wear is generated by either bond fracture
or grain fracture.
With this in mind, a statistical approach was devised to determine
the percentage
of the total wear due to bond fracture.
on the particle size distributions
It was based
for both the wear particles
the grains used for production of the wheel.
and
This statistical
approach was also applied to the analysis of abrasive particles
generated by dressing the wheel.
The following assumptions were madet
1.
There is only one bond fracture per grain.
2.
The total wear is proportional
fractures.
3.
The largest particles are due to bond fracture.
4.
The grain and bond fracture particles have the same
density.
5.
The weight of a grain or bond fracture particle is
proportional to the cube of the average particle
to the number of bond
diameter as determined by sieving.
6. The contribution to the total wear by particles
of bonding agent is negligible.
Calculation of the percentage
of total wear due to bond fracture
(hereafter called "per cent bond fracture") with the assumptions stated
above was based on the following line of reasoning.
-23-
A given weight
of wheel wear, w, corresponds
Let
to a given number of whole grains, M.
m equal the number of grains per unit weight of grinding wheel.
This is experimentally
determined
used in manufacturing the wheel.
by sieving a sample of abrasive
M is obtained by multiplying m by.w.
M is also the number of bond fracture particles in w miligrams of
wear.
The ratio (x 100) of the weight of the M biggest particles to
the total wear "w" is equal to the per cent bond fracture, B.
The per cent bond fracture also represents
the weight of an
average bond fracture particle compared to the weight of an average
whole grain. With the per cent bond fracture B expressed in decimal
form (B/100), its cube root is the ratio of the average bond fracture
particle diameter to the average whole grain diameter.
-24-
IV.
DRESSING
4.1
Introduction
Most grinding operations are very sensitive to the manner in
which the wheel is dressed.
This is especially
true in the case of
precision grinding where the depths of cut are small and the radial
wheel wear amounts to only a small fraction of the mean grain diameter.
In this investigation, two different dressing procedures were
used which are referred to as "coarse" and "fine".
Coarse dressing
was accomplished
by passing the flat side of a pyramidal diamond
across the wheel
face with
.001 inch radial infeed at 3 ft/min. cross-
feed at the same wheel/speed
inclined 13 degrees
used for grinding.
The diamond was
towards the trailing edge of the wheel.
This
procedure was repeated five times beyond what was necessary for tring
the wheel:
typically a total of ten or fifteen passes were taken.
The diamond was rotated 90 degrees after each test in order to maintain
its shape.
The fine dress was achieved in a similar manner but with two
additional
"spark-out" passes
(no downfeed) also at 3ft/min crossfeed
velocity. Although differences between these two dressing procedures
may appear to be slight, substantial differences in grinding action
were observed.
The number of active grains per unit area and the initial wear flat
area on the wheel face were determined
for both dressing techniques
-25-
using
the methods previously described.
Prior to making these measurements,
a single grinding pass across the 1018 steel workpiece was taken.
This was necessary in order to clearly view the wear flats on the
grains.
The particle size distribution was also obtained for particles
removed from the wheel during a coarse dress pass.
The per cent bond
fracture was calculated and was related to the wheel grade and the
number of active grains per unit area.
4.2
Results
The experimental results are listed in Table 3 and shown in
the graphs in Figures 4-8.
From Figures 4 and 5 it is seen that harder wheels and finer
dressing produce more active grains per square inch and a larger
initial wear flat area.
Between
the G and K grade wheels
8.6 per cent bonding agent respectively)
(3.1 and
there is about a factor of
three increase in the number of active grains, and a factor of four
increase in wear flat area.
These parameters are about 15 per cent
greater with the fine dress than with
the coarse dress.
The average wear flat area per grain is shown in Figure 6 as a
function of wheel grade and dressing condition. This is obtained by
dividing the wear flat area per square inch (.01 x per cent wear
flat area) by the number of active grains per square inch.
The wear
flat area per grain is constant for the H through K grade wheels at
-26-
a r- I bOu
1250
(NJ
I I000
z
1,,
750
IL.)
1W
(3
500
250
C)
v0
2
4
BOND
Figure 4.
6
PER CENT
8
I0
Number of active grains/inch 2 versus bind per cent for fine
and coarse dressing. (The letters denote wheel grades.)
-27-
LLJ
-j
_J
LL
Ll
3
-o
Figure 5.
2
4
6
8
BOND PER CENT
10
Wear flat area versus bond per cent for fine and coarse
dressing. (The letters denote wheel grades.)
-28-
D
o
7 -
-vO
X
zt
D
20
EL
wL
I0
.._
iLW
CE
r)
0
2
4
BOND
Figure 6.
6
8
I 0
PER CENT
Wear flat area per grain versus bond per cent for fine and
coarse dressing.
(The letters denote wheel grades.)
-29-
___
___._
100 GRAIN
LLI
U'
at
0>
80-
LLJ
bu
Al_
10
/
m
I
I
/
_
A P
&+Vr
H
I.
/
I
/
/
/
I
$ I
:
3D
20
K
DRESSING
PARTICLES
I,
w-1
C)
20
Figure
7.
40
N
1_LTTTTTTTTTTTTTTT
Lrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
...__
60
80
100 200 325 >325
SIEVE NUMBER
Particle size distribution for dressing particles and
abrasive grain.
(The letters denote wheel grades.)
-30-
I h
IUU
'
-
80
|
|
~
_
I
I
LUL
U)
~~
.%
I
w;
_
I
j
_
<:
-
60
-....
I
N..-
- i
I
tl
Z
co
I.-
I
40
!
II
I
.I
IIj
DRESS IN G
(.)
PART ICLI -S5
I.
I -
4
,.
..
.
..
_
.
_
cr:
LLJ
H
G
A
vC )
Figure 8.
2
2
l
I
i
I
J
I
li
i
I
4
6
8
BOND PER CENT
I?
I
I 0
Per cent bond fracture versus bond per cent for dressing
(The letters denote wheel grades.)
particles.
-31-
about 17 x 10- 6 inch 2 , and about one-third
lower for the G wheel.
The
wear flat area per grain for the harder wheels represents only about 8
per cent of the grain cross-sectional area which is determined from the
square of the mean grain diameter.
Figure 7 shows the particle
size distribution
for wheel particles
removed during dressing for the various grades of wheel.
ings corresponding
to the sieve numbers
parison, the distribution
The screen open-
are given in Table 4.
is also presented
for the 32A46 grain (32 Alundum,
These distributions
46 grain size) used in production of the wheels.
plotted on a cumulative basis from larger to smaller particles
to larger sieve numbers).
For com-
are
(smaller
A higher elevation of the curve corresponds
to
less fragmentation and larger particles.
The results clearly show that there was more fragmentation when
dressing
the harder grade wheels.
This can also be seen in Figure 8 where
the per cent bond fracture, which is calculated
from the particle distri-
butions in Figure 7, is plotted for the various wheel grades.
4.3
Discussion
The surface of the grinding wheel is defined by the tips of the active
grains.
In order for a grain to be "active", it mst
periphery,
say within 10-5 inch which approximates
be close to the wheel
the chip thickness.
If a
wheel is dressed in such a manner as to decrease the height deviations among
t:he tips of the outermost grains,
there are likely to be more active grains
in the surface of the wheel.
-32-
It has been shown
(see Figures 4 and 8) that the harder wheels
tend to have smaller dressing particles and more active grains. Smaller
particles
are to be expected since grains more firmly held with larger
to fragmentation
amounts of bonding agent are more susceptible
prior
The number of active grains should increase
to total dislodgement.
with increasing wheel hardness since the smaller particles leaving
the wheel would minimize
on the wheel surface.
the height deviations among the grains left
This is clearly illustrated
in Figure 9 which
is a crossplot of the active grains per square inch and 100 minus the
per cent bond fracture.
per cent bond fracture
Zero on the absicissa
(an infinitely
corresponds to 100
soft wheel).with only whole
grains removed by dressing.
The extension of this curve almost intersects the origin.
This makes sense from a physical standpoint.
In Appendix A it is
shown that the potential number of active grains is about 3240/inch2
For an infinitely soft wheel
.
this is also the number of grain tips
expected to extend to within one grain dimension of the wheel
periphery.
With the wheel periphery
wheel and the tip of the outermost
distribution
defined by the center of the
grain, assuming the height
of the grain tips is random,
of the potentially
the probability
active grains is active
periphery) it equal to 10
(mean grain diameter
5
(within 105
that any
of the wheel
divided by the mean grain diameter
.015 inch) or .0066.
The expected number
of active grains per square inch for 100 per cent bond fracture is
then .0066 x 3240 = 22, which is very small.
-33-
1500
1250
CM
I(3
1000
Ln
z
0 750
LU
-)
C2
<~
500
250
Cl
100
80
60
40
20
'0
IOo-(PER CENT BOND FRACTURE )
Figure 9.
Number of active grains per square inch versus 100 minus per
(The letters decent bond fracture for dressing particles.
grades.)
note wheel
-34-
PAGES (S) MISSING FROM ORIGINAL
PAGE 35 MISSING
V.
ATTRITIOUS
WEAR AND GRINDING
5.1
Introduction
FORCES
Attritious wear in grinding refers to the development
of wear flats on the tips of the active grains.
and growth
This type of wear is
measured by the percentage of the wheel surface covered with wear flats.
In the previous section it was seen that wear flats are dressed on
to the wheel and therefore, in this sense, the initial attritious wear
is not zero. While the wear flat area will, in general, increase as
grinding proceeds, this is not a necessary requirement since fracture
wear can diminish the wear flat area.
Grinding forces are measured with the semiconductor
strain gage
dynamometer previously described, and each data point is the average of
an "up" and "down" pass.
"Up" grinding refers to the condition where the
workpiece velocity, v, is in the opposite direction to the wheel velocity,
V, at the grinding area.
motion.
"Down" grinding
refers to the opposite table
In the present series of tests, the grinding forces were only
slightly affected by the direction of the workpiece motion, the "down"
grinding forces being at most 10 per cent greater at the largest wear flat
area.
5.2
Results
Experimental
results are presented
n Tables 5 and 6 and Figures 10-
14 for the 1018 steel with the fine and coarse dressed wheels.
Figures
10 and 12 show the variation in the grinding forces and force ratio and
-36-
A
LL
.5
tn0
m
O
rJ
oI
>0
L3 0
LL
*J
C
10
O.
-0
20
40
60
80
100
PASSES
1018 STEEL,) FINE DRESS
oG
OH
al
+J
XK
Figure 10.
Grinding forces and force ratio versus number of passes for
1018 steel workpiece, fine dress, V - 6250 ft./min., v
8
ft./min., d - .001 in. (The letters denote wheel grades.)
-37-
CO
< bo
cax 60
.
40
< z 20
H
-
aL
20
LLU
af
Ll
I
4
I
2
n
"'IO
60
40
20
80
100
PASSES
FINE DRESS
1018 STEEL)
G
Figure 11.
A1
OH
+J
XK
Per cent wear flat area and wear flat area per grain versus
number of passes for 10-18 steel workpiece, fine dress, V .001 in. (The letters
6250 ft./min., v - 8 ft./min., d
denote wheel grades.)
-38-
I0
__
_
LL
c
5
LL
0
-
I10
=zzz6
Tz-__
0
LL
m30
_J
m
t)
>
x
20
IL
I10
-
rM
N it
n
0O
20
40
__x-
- ----iff -0 ----o
C-
60
80
100
PASSES
1018 STEEL)
OG
COARSE DRESS
aH
xK
Figure 12. Grinding forces and force ratio versus number of passes for
1018 steel workpiece, coarse dress, V - 6250 ft./min., v -
8 ft./min.,
d - .0OI in.
-39-
(The letters
denote wheel grades.)
c)
6C
I'
< W
40
z
LL -
--
-e O
20
L
<-
.,.
....
LU
X
___.'--.
C'
--
--
-I"-"--
S
LU:
X~
6
-
-J
LL
~~~~~
-
.I
4
X--..
LU
2
0
----x
ci - -._
_ . .. .......
..
...---....-
0
20
1018
4
6
PASSES
STEEL
I
80
_o_
100
COARFSE DRESS
oH
Figure 13.
Per cent wear flat area and wear flat area per grain versus
number of passes for 1018 steel workpiece, coarse dress, V 6250 ft./min., v
8 ft./min., d - .001 in. (The letters de-
note wheel grades.)
-40-
r,
IDW
1251
I
z 100
0
- 75
,
5
2 50
25
0
Figure 14.
2
6
4
BOND PER CENT
8
10
Number of active grains/inch 2 versus bond per cent for 1018
.001
steel workpiece, V - 6250 ft./min., v - 8 ft./min., d
in.
(The letters denote wheel grades.)
-41-
Figures 11 and 13 the variation
number
in wear flat areas as a function of the
of passes for the different grades of wheels.
The wear flat area
data points for 1 pass, Figures 11 and 13, are those presented in the previous section in Table 3.
To simplify the-graphs, only the results for the
G, H, and K wheels are plotted in Figures 12 and 13.
The number of active
grains was more or less constant as grinding proceeded,
and therefore, the
average values are presented in Figure 14 for the different wheel grades
and dressing
techniques.
The grinding forces in Figures 10 and 12 are characteristically higher
for the harder grades of wheels.
where the grinding
With the harder wheels a transition appears
forces increase rapidly, the rate of increase being about
seven times greater for the vertical as compared
to the horizontal
force
component. This transition is more readily obtainable with the finer dressing technique where it occurs almost instantaneously
for K-grade wheel, after
about 35 passes for the J-grade wheel, and after about 60 passes with the I-
grade wheel.
At this point workpiece "burn" is
surface takes on a bluish tempering
observed where the ground
color.
The wear flat area measurements in Figures 11 and 13 follow the same
general
trend as their corresponding
force measurements.
As previously
stated,
the number of active grains per unit area for each wheel was found to be rel-
atively unchanged as grinding proceeded. Therefore increases in the wear
flat area with the number of passes would be expected to be primarily due
to the growth of existing wear flats rather than the development of new ones.
This can in fact be seen in Figure 15 where photographs
-42-
of the same area of
40 passes
20 passes
80 passes
60 passes
100 passes
20X
Figure
15. Microphotographs
of wear flats after 20, 40, 60, 80, and 100
fine
passes. Wheel - 32A461I8VG, workpiece - 1018 steel,
dress, V
=
6250 ft./min., v = 8 ft./min., d
-43-
.001 in.
a grinding wheel are shown after 20, 40, 60, 80, and 100 passes.
Although little variation was noted in the number of active grains
as grinding proceeded, substantial differences were found for wheels of
different grades, the harder wheels exhibiting more active grains. A
smaller increase was generally obtained with finer dressing.
presented
in Figure 14, are substantially
These results,
the same as those previously pre-
sented in Figure 4.
Figure 16 presents cross plots of the horizontal and vertical
nents of the grinding forces, FH and FV, each plotted against
wear flat area,
A.
compo-
the per cent
The data for all grades of wheels using both dressing
techniques fall on a single curve consisting
of different slopes.
The straight
of two straight line segments
lines in this figure
were obtained by the
method of least squares with the force taken as the error free variable.
intersection
of these two straight line segments, at about 3.6 per cent wear
flat area, corresponds
observed.
The
to the transition
above which workpiece
Data points used for determining
"burn" is
this section of each of the curves
were the ones where burning was actually observed,
as indicated in Tables 5
and 6.
The relationship
between the grinding forces and the per cent flat
area was also obtained for the other workpiece materials
listed in Table 2
for the same grinding conditions, and for 1018 steel with both the wheel
speed and table speed decreased by a factor of 2.
sented in Figures 17-23 and Tables 7-13.
-44-
These results are pre-
1018 STEEL
0
v' RTICAL
FORCE)
FV
4( 1
-
H O RI Z NT XL FORCE,
F
H
o
on
o
o
o0
-J
LU
LIL
0o
-_7
Z
2
0o
cc
0D
o
I
0
0
v0
Figure 16.
4
2
WEAR FLAT AREA,
6
A
8
)O7Q
Grinding forces versus wear flat area for 1018 steel, fine and
coarse dress, V - 6250 ft./min., v - 8 ft./min., d - .001 in.
(The letters denote wheel grades.)
-45-
52100 STEEL
FV
4
FH
n
I
,-3
0
LL
O
z
2
0,
(D
0
I
0
I
v0
4
2
6
8
WEAR FLAT AREA,A o/
Figure 17. Grinding forces versus wear flat area for 52100 steel,
dress, V - 6250 ft./min., v - 8 ft./min., d - .001 in.
-46-
fine
4
_--I
.
(I J
(-7
i L._
Z'
Z
1
4
I,:
x~~
1
WEAR
Figure 18.
FLAT
AREA) A,
0
Grinding forces versus wear flat area for T1 steel, fine
dress, V - 6250 ft./min., v - 8 ft./min., d - .001 in.
-47-
40
co
_J
'30
IL
C)
11
z
D
z
20
(3
I0
0
Figure 19.
2
WEAR
6
4
F LAT
AREA
,A
8
,)
Grinding forces versus wear flat area for 130A titanium, fine
dress, V - 6250 ft./min., v - 8 ft./min., d = .001 in.
-48-
40
_J
w 30
LJ
Cr
z
D 20
z
10
0
2
WEAR
4
6
8
FLAT AREA) A, jo
Figure 20. Grinding forces versus wear flats area for niobium, fine dress,
V - 6250 ft./min.,
v - 8 ft./min.,
-49-
d - .001 in.
40
tcn
-J
LL
0
U-
L220
a
I
z
D0
I0
n
2
4
WEAR FLAT AREA,A,
0
Figure 21.
Grinding forces
dress,
V - 6250
6
To
versus wear flat area for molybdenum, fine
.001 in.
8 ft./min., d
ft./min., v
8
0
O
40
STELLITE 6B
o FV
O
FH
J
, 30
o
0
()
LL
z
0
20
O
0
O
w3
O
0
m
I10
M
/
I
/
/-'.
'
0
0
I
I
I
I
2
4
6
WEA R
Figure 22.
FLAT AREA
,
t,:
Grinding forces versus wear flat area for Stellite no. 6B,
fine dress, V - 6250 ft./min, v - 8 ft./min., d - .001 in.
8
40
J)
IS
,_1
LL3 0
C'
(D
0a
I10
,
0
2
WEAR
Figure 23.
4
F'aT
8
Ao
AIREA,
Grinding forces versus wear flat area for 1018 steel, fine
dress, V - 3125 ft./min., v - 4 ft./min., d = .001 in.
For the steel workpieces
(Figure 17, 18 and 23) the same general
behavior was observed as in Figure 16, and workpiece burn was always
observed beyond the transition. The results for-the other materials,
Figures 19-22, all fell on a single straight line.
An attempt was made to grind a number of other materials including
nickel, cobalt, copper, bronze, brass, and aluminum.
the phenomepon
For these materials,
commonly referred to as "loading" occurred where fragments
from the workpiece would stick to the wheel and prevent normal grinding
action.
With the eception
Under these conditions,
5.3
of the cobalt, no grinding sparks were observed.
it was impossible
to obtain any meaningful
data.
Discussion
The experimental
results for the force vs. wear flat area relation-
ships, with the exception of those for the Stellite, are consistent with
the following interpretation. The vertical and horizontal grinding forces
are both made up of two components,
one due to cutting and one due to
sliding on the wear flats.
FV ' FVC + FVS
(5.1)
FH '
(5.2)
FHC +
FHS
This is illustrated in Figure 24.
The chip mechanics
and therefore the
cutting force components are assumed to be unaffected by the size of the
wear flats.
At zero wear flat area, the sliding forces are zero and the
grinding forces are equal to the cutting force components, FVC and FHC.
-53-
GRAIN
CHIP
-FHS
----
V
"FHC
FVC
FVS
WORKPIECE
Figure 24.
Illustration
of chip formation and the cutting and sliding
force components.
-54-
The linear increase of the vertical
force with-wear
flat area (only
up to the transition for steels) indicates that the average contact pressure
p between the wear flats and workpiece
is
force also increases linearly with wear
sliding friction
j
is also constant.
constant.
Since the horizontal
flat area, the coefficient
of
Defining aR as the real area of
contact between the wheel and the workpiece,
equations 5.1 and 5.2 then
become
FV
FVC + aRP
(5.3)
FHc + aRp
FH
The actual wear flat pressure
(5.4)
dFv
dA
can be calcultated from the slope
and a consideration of the grinding geometry,
Figure 25.
area of contact between the wheel and the workpiece,
The apparent
aA, is given by the
expression
aA = l
where
1
l
c
x b
(5.5)
is equal to the undeformed
1
=-/D
chip length ( 29 )
d
(5.6)
and b is the width of the workpiece.
wheel and the workpiece,
The real area of contact between
the
aA, is equal to the product of the fraction of the
total area covered with wear flats and the apparent area of contact,
aR
.01 A x aA
(5.7)
-55-
WHEEL
FH
FV
WORKPIECE
Figure 25.
Illustration
of the grinding geometry.
The average pressure p is then
dFv
- da .O1
dF VS
P =
r
dR
R
V
The friction coefficient
dFH/ dA
Fvs
dFV/ dA
ing operations.
(5.8)
is given by
FHS
The same interpretation
b x 1
dFv
d
dA
(5.9)
can also be applied to other types of grind-
Story (30) has recently shown that forces obtained with
coated abrasives, for both fixed feed and constant force grinding,
considered as the sum of cutting and
can be
Although the
sliding components.
they are rela-
origin of the sliding forces is not discussed, presumably
ted to the size of the wear flats.
(14)
has found that for controlled
Hahn
is
constant),
force cylindrical grinding
(FV
the metal removal rate decreases in direct proportion to the
increase in the wear flat area.
This can be explained by assuming
that the
average wear flat pressure is constant- and the fraction of the controlled
vertical
force employed in the cutting action, Fvc/Fv, is proportional
to the metal removal rate.
From Hahn's data on 52100 steel, I calculate
the average wear flat pressure to be about 7000 lbs./in.
Yoshikawa
(8 )
has stated that below
are constant and independent
the transition, the grinding forces
of the wear flat area.
of his data reveals that this is
.
not true.
A closer examination
Force vs. wear flat area curves
were presented only for the harder grades of wheels and the grinding forces
measured in the first
few passes were incorrectly
-57.-
assumed to correspond to
zero wear flat area.
(See Figure 5).
He did obtain smaller grinding
forces with soft wheels but no wear flat area measurements were reported
for these.
An analogous situation has been observed in the case of turning where
the cutting forces are found to increase linearly with the area of the
wear land (31, 32, 33, 34).
pressure between
Zorev (3 4
)
has pointed out that the contact
the wear land and the workpiece
"can be considered elastic
since the plasticity
condition is fulfilled only at the cutting edge where
the contact stresses
reach a maximum".
To visualize this more clearly consider the wear land as a punch with
a plane base on an elastic semi-infinite
plane, Figure 26, where P is
the
total contact force per unit width, 2 a is the contact length, and x is the
local variable.
by the formula
The elastic pressure
distribution under the punch is given
(35 )
x
P(a
P
a
(5.10)
l-
(x)2
a
Thus at the corners of the punch, x
+a, the pressure is infinite,
How-
ever, in reality, there is plastic deformation in these regions, and the
pressure will approximately
follow the dotted lines reaching the full in-
dentation hardness H at the corners of the punch
which follows, the size of the plasticity
. In the discussion
region is assumed to be much
smaller than a.
In the case of a wear land on a cutting tool or the wear flat on a
grain, full plasticity will probably be reached only at cutting edge
( x = - a) and the pressure towards the trailing edge, x = + a, would be
-58-
P
T
H
H
-a
Figure 26.
+0
Pressure distribution due to contact between a punch
a semi-infinite elastic solid.
and
less than H.
In this case, the pressure distribution
is given by an
expression of the form
P ( a)
(5.11)
f(aa
2a
and
p
2a
-
(5.12)
If the shape of the pressure distribution
of 'a' and the boundary
f( a ) is independent of the size
a
-a is fixed-by. the hardness H, then
condition at x
equation 5.11 is also independent of a'. The average pressure is then constant and proportional
to the workpiece
hardness H.
In Figures 16-23, the straight lines were determined by the method of
least squares with the force taken- as the error free variable.
These re-
sults are summarized in Table 14 together with the standard errors, correlation coefficients
specific
flats qF
c, cutting forces, cutting force ratios
cutting energies uc, and the frictional
The specific
U
c
(FHC/Fvc)
energy flux on the wear
cutting energy is given by
FHC V
-
(5.13)
vd
and the frictional energy flux by
qf
(5.14)
p V.
Note that the correlation
coefficients
the straight line approximation
are close to unity which means that
is valid.
-60-
Figure 27 shows a cross plot of the specific cutting energy and the
average wear flat pressure. Materials which reqire a larger cutting energy generally experience
vious discussion,
a greater contact pressure.
In line with the pre-
such a correlation would be expected
to be valid only to
the extent that the cutting energy describes the plasticity condition under
the cutting edge of the grain.
The results for the T 1 high speed steel
fall outsAde this general relationship
possible because of its high alloy
content. At the peak temperature generated at the chip which is near the
melting
temperature of the workpiece,
be relatively
unimportant
energy as 1018 steel.
and the T1
Calculation
steel requires about the same cutting
At the lower temperature under the cutting edge, the
alloy content becomes significant
steel.
the alloy content of the steel should
and T1 would be relatively harder than mild
of the grinding
temperatures
are presented in the next
section.
With the 1018 steel run at half the speed, the cutting energy is
approximately the same as that found at the higher speed.
tact pressure is about twice as big.
However, the con-
This suggests a dynamic effect whereby
decreased grinding speeds raise the contact pressure and, in effect,
move
the curve in Figure 27 to the right, possibly far enough so that it will
intersect the origin.
This dynamic effect could account for the improved
grinding performance which
has been observed at very high grinding speeds (36)
When the specific cutting energy is plotted against the melting temperature of the workpiece material
ear with the curve passing
(Figure 28) the result is approximately
through the origin.
-61-
(Melting temperatures
lin-
for the
8
.
0O
Nb.
z7
ro
)
6
u5
5210
1018
4
z
z
3
-
2
250 FT./MIN.
v=8 FT,,/ MIN.
V =6
LL
d =.001
I
IN.
a,
O
ra
--
VW0
WEAR
Figure 27.
I
5
I
10
I
I
15
20
FLAT PRESSURE,), LB./IN2?XI03
Specific cutting energy versus wear flat pressure.
0
x 8
.
)
I .
I1
52
*1018
4
/
z
/
a0
/
/
--
A
2
/
/
/
/.
/
LL
/
/
U
A
lA
r
0i vCI
I
1000
I
2000
MELTING POINT,
Figure 28.
3000
OK.
Specific cutting energy versus melting point of the workpiece.
alloys are given by the melting
result
temperatures of their base metal).
This
is not altogether unexpected since a high melting temperature
signifies strong bonding.
It can also be seen that all the steel alloys
require roughly the same cutting energy. At the high temperatures generated in grinding chip formation, which will be shown to be near the melting temperature, the effect of alloying
and prior heat treatment should be
relatively unimportant.
It is interesting
to note that all the metals which were found to
load the wheel have a melting
temperature below that of iron.
Hence no
data points are given in Figure 27 for the lower end of the curve.
Why
wheel loading should occur with these-materials is not understood.
Workpiece burn, which appears at a critical wear flat area for a particular steel, is characterized
bluish
by sharply increasing grinding forces and
tempering colors on the workpiece.
ridge of material
is also observed
In addition
to this, a flash or
to form along the edge of the workpiece
which indicates that some of the material
to be removed is ploughed aside
by the grains instead of being formed into chips.
Metallurgical
examina-
tion of burned workpieces by Littman(3 7 ) and Tarasov(3 8 ) have shown that
the surface layers are over tempered and softened.
The burn color is the
result of surface oxidation at high temperature. Apparently this metallurgical softening,
and non-metallurgical
tures in grinding,
softening due to the high tempera-
lead to a fully plastic condition under some of the
wear flats, and the slope of FV vs. A beyond
pond to the hardness
under the grain.
the transition would corres-
These pressures
are about 10 times
greater than the average wear flat pressures below the transition.
-64-
The
drop in friction coefficient
above the transition
(Table 14) is also
to be expected.
Littman( 3 7 ) has empirically found that the surface temperature in
grinding TG, is uniquely
related to the energy input per unit area of
work surface ground, or
G
FV
1ccb
(5.15)
Referring to Figures 16, 17, 18 and 23 it is seen that the transition
did occur at approximately
the same energy input rate (FHV) or in other
words; the workpiece burn did commence at approximately the same temperature in all four cases.
With the Stellite workpiece
a flash of material also forms as in
the case of steel workpiece burn.
the vertical
Looking
at Figure 22, the extension of
force curve to zero wear flat area would result in a negative
value of the force, FVC.
In reality this could not exist and the curve
must turn toward a positive value.
grinding this material
The wear flats grew so fast when
that data below a
cent could not be obtained.
and the flash formation,
Considering
wear flat area of about 1 per
the shape of this force curve
the grinding mechanism here is probably
as that for steel beyond the transition.
-65-
the same
VI.
GRINDING TEMPERATURES
6.1
Introduction
Some of the most serious problems
by grinding heat.
in the grinding process are caused
Grinding burn with steel is associated with softening
of the surface layer or in severe cases, softening
Cracking
is often observed
in the ground surface as a result of the rapid
cycle of heating and cooling.
difficult
The desired dimensional
accuracy may be
to obtain because of the thermal expansion of the workpiece.
Control of these problems is usually accomplished
However, a fundamental understanding
is needed
followed by rehardening.
by using coolant.
of grinding heat and temperatures
to provide a broader approach
to their solution.
It has been shown that the total grinding energy can be considered
as the sum of frictional energy due to sliding on the wear flats and
cutting energy due to chip formation
the cutting energy is associated with
(Figure 24).
To be sure, part of
frictional processes but this is
not to be confused with the sliding energy considered here.
wear flat area increases, the additional
dissipated
as heat at the interface between
There has been some confusion
in grinding.
theory
energy required is
the grain and the workpiece.
about the concept of surface temperatures
Outwater and Shaw (39) used Jaeger's moving heat source
(40) to calculate
the temperatures on the shear plane of the chip.
Their results are questionable
assumed
grinding
As the
to be associated
insofar as the total grinding energy was
only with cutting
-66-
(FHS
O0). Sato (4 1
)
used the
concept of an instaneous heat source over the total grinding area (apparent
area of contact) to determine an "average" surface temperature.
(37)
Littman
positioning
experimentally determined grinding temperatures by
a thermocouple at the bottom of a hole
(.021 or .026 inch
diameter) which extended nearly to the ground surface. Temperature
measurements
(TG in equation 5.15) seem to be
obtained in this way
closely related to some metallurgical
changes in the ground surface.
However the cross sectional area of the hole was so large, compared
a grinding
chip or wear flat, that the relationship
and the actual temperature distribution
In this section, the distribution
to
between this temperature
on the surface cannot be determined.
of surface temperatures
in the
vicinity of the chip and wear flat (for an isolated cutting point) will
be calculated as the sum of two moving heat sources, one at the shear
plane of the chip and
additional
the other on
the wear flat.
There is also an
temperature rise due to all the other cutting points which is
calculated as a single moving heat source equal to the apparent area of
contact.
6.2
Geometry of Chip Formation
As a first step it is necessary to consider the geometry of chips
formed in the grinding process.
subject can be found in reference
undeformed
The details of the treatment of this
(26),
To a good approximation,
grinding chip can be considered
width as shown in Figure 29.
the
as a long wedge of constant
The undeformed
chip length 1
c
is given by
(t ,) max
J(
I~~~~~~~~~~~~~~
--
---
Ic
UN DEFOR MRME
D
CHIP
Figure 29. Geometry of the undeformed chip.
-68-
the chordal length
1
and the maximum undeformed
=
(6.1)
VDd
chip thickness by'
/
(t)max
1] 2
(6.2)
w here
D = wheel
diameter
d - downfeed per pass
V - wheel speed
v
table speed
C
number of cutting points per unit area
r
chip
ratio of width to thickness of undeformed
From taper section studies of ground surfaces
r, which is
(26)
,
the value for
chip thickness to width, has been
the ratio of underformed
found to be about 15.
As previously
discussed,
the number of cutting points per square
inch, C, has been often confused with other wheel parameters.
The only
direct measure of this value was achieved by Grisbrook(2 8 ) where the
value of C was actually determined from the number of chips generated.
For a 46 grit wheel, a typical value for C has been found to be about
6000 per square inch.
This is higher than values obtained by other
methods which supports the contention
that there can be more than one
wear flat per grain and more than one cutting point per wear flat.
-69-
For the present case (D - 8 in., d = .001 in., V = 6250 ft./min.,
and v
8 ft./min.) equations 6.1 and 6.2 give
-
(8) (.001)~
.09 in.
(6.3)
and
(8)
(tl)max
(6250)(6000)(15)
The dimensions
of the undeformed
8
)
15
25
x 10 6
25 x 10
in.
(6.4)
chips are of course different
from those of the chips actually produced.
Grisbrook
(2 8 )
has observed
that the ratio of the real chip length to the undeformed chip length is
about .1.
Neglecting
undeformed
chip thickness t
chip sideflow,
this suggests that the ratio of the
to the actual chip thickness t2 is also about
.1. Further supporting evidence is given by Brown (4 2 ) who, for chips
produced with single grains, found that this ratio is usually between
.05 and .15, again
.1 being a typical value.
In other words,
the chip
produced is about-10 times thicker than the undeformed chip.
With this, the shear angle
in Figure 20 can be easily determined
to be
*-
tanl
.1
(6.5)
or
6° .
(6.6)
-70-
6.3
Energy Partition
The grinding temperature distribution
is calculated by considering
the shear plane and wear flat areas as moving heat sources on the workpiece surface which move at a velocity
(Actually the velocity
equal to V.
For this calculation
should be V + v, but since V>, v, v is neglected.)
it is necessary
to know that heat fluxes which cross the shear zone AB
and wear flat AD into the workpiece
R 1 of the cutting energy conducted
That is, the fraction
(Figure 30).
to the workpiece
at shear zone and
the fraction R 2 of the sliding energy conducted to the workpiece at the
wear flat must be determined.
determination
Experimental
reasoning.
Both R
and R 2 should be relatively
of the wear flats, and virtually
to the workpiece
of these values is based on the following
unaffected by the size
all the sliding energy should be conducted
as heat since the steel workpiece
is a stationary heat
source, has a much higher thermal conductivity than aluminum oxide, and
has a much bigger volume.
In turning,. R 1 is typically on the order of
.20 but will probably be greater here due to the relatively small shear
angle in grinding.
The fraction of the total grinding energy conducted
to the workpiece has been experimentally
insulating the workpiece
and measuring
determined
its average temperature rise after
one pass by means of a thermocouple attached
piece.
for 1018 steel by
Wear flat areas were also measured.
to the center of the workThese results are listed in
Table 15 and plotted in Figure 31, where the straight line relationship
is obtained as expected.
The fraction R 1 is the value of R at zero wear
-71-
GRAIN
-
A
-
RUBBING
WV
WORKPIECE
Figure 30. Geometry of ship formation.
D
I.00
1
1I
I
.80
l
w
----
-
-V
·-
-
I
I
I
I
-
-
5l
O'I
i
(3
nf
U .60
so
I
IO,
-
I
----
I
I
I
i
I
-
-
--
-
--
-
-
"
-
I
L-
z
LU
.40
:
I~~~~~~~~~~~~~~~~
1018 STEEL
FINE DRESS
.20
V=6250
v=8 FTMIN.
LU
d
_ _
1
_
_
2
= .001
I
IN.
I
4
3
WEAR FLAT AREA,
Figure 31.
FT./MIN.-
A
5
)1
Fraction of grinding energy conducted to the workpiece versus
the wear flat area.
flat area which is approximately
Comparing the slope of
equal to .61.
this line with that of FH vs A in Figure 16, the value of R 2 is found to
be equal to .97, or virtually
heat to the workpiece.
all the sliding energy is conducted as
As a thermal analogy,
this presents additional
of the grinding forces as the
evidence to support the interpretation
summation of cutting and sliding components.
Sato (4 1 ) has measured R for cylindrical
grinding also by measuring
the temperature rise of the workpiece and has given a value of .85.
Similar values have also been obtained by other Japanese researchers(4 2 )
and are in the same range as those presented
6.4
here.
Calculated Grinding Temperatures
Jaeger's
theory of moving heat sources
the temperature
is based on the assumption
workpiece
considered
will be used to calculate
rise on the ground surface at the chip and wear flat
for the 1018 steel near the transition
approach
(40)
(A = 3.5% in Figure 16).
This
that the thermal properties of the
do not change with temperature.
For the temperature ranges
here, this is really not the case, and the variation
of thermal
properties with temperature are shown in Figure 32 for data taken from
reference
(44).
However, a reasonable
approximation
to the actual
situation can be obtained by using this constant property solution with
the thermal properties evaluated at the average surface temperatures
In the present case, the thermal properties
will be found to be lower than the average
at 12000F will be used which
temperature at the chip but
higher than the average temperature on the wear flat.
-74-
(39)
-H
I
i
_L
25m
LL
(36
LU
r
aI2
20o
C
H
15<
-<
U
9
10-
z
) 2
( _
m
m
5c
x
CY
-
o,
I
0
500
I
1000
TEMPERATURE
Figure 32.
I
1500
n
2000
,OF
Variation of thermal conductivity and thermal diffusivity
.Data taken from Referwith temperature for mild steel.
ence (44).
The temperature rise TC due to the cutting energy is considered as
a band source of width t2 moving along the workpiece surface at the
wheel velocity V.
Since the shear angle
AB will be approximated by AC.
is small (Figure 30) the band
The calculation will be performed where
the cut is 50 per cent completed or t1 is half (tl)max.
Then the width
of the band for this case, (t2 ) 50 is equal to
(t2)50
=
(.50) (10) (tl)
=
125 x 10 6 in.
(6.7)
The energy flux across the band into the workpiece is equal to R1 times
the average cutting energy per chip divided by the average chip cross
sectional area.
Appendix
The details of this calculation are presented in
B.
In a similar way, the temperature rise T S due to sliding is calculated
as a band cource of strength R2 times the sliding energy qf (qf is given
in Table 14) moving at the velocity V.
of the grinding wheels,
From observations of the face
the wear flats at this wear flat area (A = 3.5%)
are typically about .004 inch, and this value is used for the band width.
These calcualtions are presented
in Appendix C.
Both of these temperature distributions
shown in Figure 33.
and their superposition are
Curve (a) is the temperature rise due to cutting
and curve (b) is due to sliding.
Zero on the abscissa represents the
cutting edge, with the chip to its left and the wear flat to its right.
Note that this scale is distorted with the chip magnified
compared to the wear flat.
-76-
20 times
2500
2000
*
-
L_
0
LI
Ilcn
I
"
V V
CHIP
GRAIN
-1
rar
LLJ
a-1000
i,!
500
-
a
16 b
n
v.15
.10
.05
DISTAN CE
Figure 33.
p
I
I
0
w
1
I
I
I
2
3
4
FR OM CUTTING
EDGE,
IN.XIC 3
Distribution of calculated grinding temperatures along workpiece surface. Curve (a) is for temperature rise due to cutting, curve (b) is for temperature rise due to sliding.
-77-
The peak temperature rise occurs at the shear plane and can approach
the melting point (2798 F.) of the steel.
The temperature rise over
most of the grain is smaller, with the major contribution
still due to
the cutting.
There is an additional
temperature TA due to the cutting and sliding
of other grains in the grinding area.
This is approximated by a band
source moving at the workpiece velocity v, having a width equal to the
undeformed
chip length 1c, and the strength equal to R times the total
grinding energy.
This calculation presented in Appendix D gives a
maximum value
(TA)max
=
7210°F
and an average value
(TA)ave
The average value,
5380F
(TA)ave )can be interpreted
temperature which a grit "sees".
as the average initial
The actual grinding temperatures would
then be about 500 degrees above those given in Figure 33.
-78-
VII.
7.1
SURFACE FINISH
Introduction
Grinding is often employed as a finishing process where accurate
surfaces of good finish are required.
Consequently it is important
to understand the factors which affect the quality of the surface
produced.
7.2
Results and Discussion
The surface finish generated during grinding was measured every
twenty passes for the 1018 steel workpiece using both the "course" and
"fine" dressing techniques.
These measurements were obtained
simultaneously with the data previously presented in Tables 5 and 6.
The test results are presented in Table 16 and plotted in Figure 34
for the different wheel grades.
It is interesting to compare these
results with those in Figures 10 and 12.
With the fine dress a good
surface finish in the range of 10 to 15 microinches
is obtained below
the transition, with very slight improvement noted with harder wheels.
Beyond the transition, where burning occurs, the finish deteriorates
rapidly to about 30 or 40 microinches.
The coarse dressed wheels give a much poorer surface finish than
the fine dressed wheels below the transition.
wheels
give a slightly improved finish.
-79-
Here again, the harder
1018
*FINE
STEEL
o COARSE DRESS
DRESS
30
K
15
O0
30
zz 15
J
3O
30
o
[i 15 ___
__
0
30
G
0
20
60
40
80
100
PASSES
Figure 34.
Surface finish versus the number of passes for fine and coarse
8 ft./min.,
dressing for 1018 steel, V - 6250 ft./min., v
d - .001 in. (The letters denote wheel grades.)
-80-
Theoretical considerations
of the finish produced in surface
grinding have often been based only on the geometry of the undeformed
chips.
Orioka (45)and Nakayama and Shaw (4 6 ) considered this problem
both theoretically and experimentally
and determined that the height
differences between the tips of the active grits is usually a more
significant factor.
This is consistent with the present findings
where, in the absence of workpiece
burn, the "fine" dressing
produces a significantly better significantly better surface finish.
The two additional spark out passes for fine dress apparently reduce
the height difference among the active grains.
-81-
VIII.
8.1
FRACTURE WEAR
Introduction
Grinding wheel wear is usually determined as the decrease in the
radius of the grinding wheel.
As previously mentioned, the wheel wear
before redressing usually amounts to a small fraction of a grain
dimension, yet it will be shown that a significant portion of the wear
consists of particles almost as big as whole grains.
Determination of
wheel wear from the weight of the abrasive particles removed, and a
study of their size distribution,
therefore provides a more fundamental
approach to the study of grinding wheel wear.
In this section, the results of the grinding wheel wear studies are
presented for the 1018 steel using both the "fine" and "coarse" wheel
dressing and for the 52100 steel using the "fine" dressing.
analysis of the wear particles was performed
of bond fracture.
A sieve
to determine the amount
A quantitative relation was obtained between the
grinding wheel wear and the grinding forces.
8.2
Results
The test results are presented in Tables 17-19 for the 1018 steel
with the fine dress, 1018 steel with the coarse dress, and 52100 with
the fine dress respectively.
The accumulated wear is plotted against
the number of passes in Figures 35-37.
-82-
200
E 150
I
w 100
J
D
< 50
n
"0
20
40
60
80
100
PASSES
Figure 35.
for 1018 steel,
Accumulated wear versus the number of passes
d - .001 in.
v
8
ft./min.,
ft./min.,
V
6250
fine dress,
grades.)
(The letters denote wheel
-83-
200
150
a
_J
< L'I050
WO
20
40
60
80
100
PASSES
Figure 36.
Accumulated wear versus the number of passes for 1018 steel,
coarse dress, V - 6250 ft./min., v - 8 ft./min., d - .001 in.
(The letters denote wheel grades.)
-84-
200
c 150
3
<~
LI.
0U
100
-J
D
D
(L)
()
50
C
v0
20
40
60
SO
100
PASSES
Figure 37.
Accumulated wear versus the number of passes for 52100 steel,
fine dress, V = 6250 ft./min., v = 8 ft./min., d = .001 in.
(The letters denote wheel grades.)
or
It appears that the wear rate curve is characterized by three
distinct regimes, all of which are evident in the results for the I-grade
The first regime shows a high initial run in wear.
wheel in Figure 35.
This is followed in the second regime by a more or less constant but
smaller wear rate.
In the third regime, the wear rate rises again.
This increasing wear rate corresponds
previously mentioned.
to the transition or grinding burn
For both J- and the K- grade wheels
(Figure 35))
In
the grinding force transition occurs near the beginning of the test.
this case, only the third wear regime can be clearly observed.
With the coarse dressed wheels and the 1018 steel workpiece
(Figure 36), only the first and second regimes are clearly visible except
after 80 passes with the K-grade wheel where burning occurred.
maximum wear was obtained with the intermediate
The
I-grade wheel.
The results for the 52100 steel (Figure 37) clearly show only the
run-in a steady state wear, and the harder wheels experienced less wear
than the softer ones.
Workpiece burn did occur after about 60 passes
with the K wheel and 80 passes with the J wheel, but the third wear
regime did not appear.
The size distributions of abrasive wear particles are presented
Figures 38-40 for the different wheel grades.
in
The distribution for the
wheel abrasive particles is also given for comparison.
As grinding
proceeded the particle size distribution remained relatively unchanged
and the curves are for the total wear in 100 passes for each wheel.
per cent bond fracture corresponding
The
to each of these distributions is
presented in Figure 41.
-86-
100
LL
U0
Co
0 80
U
Z
LLJ
(I
LL
60
-J 40
1:,
I
20
LL
n
20
40
60
80
SIE VE
Figure 38.
100
200 325 >325
NUMBER
Particle size distribution of wear particles and abrasive grain
8 ft./
grain for 1018 steel, fine dress, V - 6250 ft./min., v
grades.)
wheel
denote
letters
(The
in.
.001
d
min.,
0_7
A!
1(U
GRAIN
n
0
80
/
Z
LLJ
Ld
LL
60
,
/
/
I
F-
J
40
K
I
1018 STEEL
COARSE
20
DRESS
.
LdJ
n
20
Figure 39.
Ii
40
60 80
SIEVE
100 200 325
>325
NUMBE R
Particle size distribution of wear particles and abrasive grain
for 1018 steel, coarse dress, V - 6250 ft./min., v - 8 ft./min.,
d - .001 in. (The letters denote wheel grades.)
_-Q_
I00
a:
<
-.Z
LU
3 60
LI
(-.
I20
j40
LJ
D
Li
20
40
60
80
SIEVE
Figure 40.
100 200 325 >325
NUMBER
Particle size distribution of wear particles and abrasive
grain for 52100 steel, fine dress, V - 6250 ft./min., v 8 ft./min., d - .001 in. (The letters denote wheel grades.)
-89-
I
^
^
IUU
LU
_1,.
80
LL
0
60
Z7
40
LJ
20
LU
0.
"0
2
4
6
8
BOND PER CENT
Figure 41.
Per cent bond fracture versus bond per cent for wear
_particles. Corresponds to Oarticle size distributions
given in Figures 38 - 40. (The letters denote wheel
grades..)
I
As in the case of dressing particles
(Figures 7 and 8), the harder
wheels generally have larger wear particles.
Presumably, this is again
due to the fact that with harder wheels with more bonding agent, a
fracture within
at the bond.
the grain is more likely to occur before dislodgement
The wear particles are slightly bigger than the dressing
particles, Figure 7.
8.3
Discussion
Most of the grinding wheel wear consists of particles which are
almost as big as the initial grains.
This observation has formed the
basis of the statistical analysis of the particles where it has been
assumed that the overall wear rate is proportional to the rate at which
bond fractures occur.
Since the bond material is a brittle substance,
the rate at which the bonds are fractured should depend in some way
upon the maximum tensile stresses in the bond bridge.
Consider an active grain in the wheel surface (Figure 42) which is
subjected to a horizontal force fH and a vertical force f
a positive bending stress which is porportional
bond at the plane AB.
stresses at AB.
Likewise,
Due to fH,
to fH is induced in the
the vertical force f
induces compressive
The maximum tensile stress in the bond is then given by
at
=
C1 fH - c2 fv
where c1 and c2 are constants.
-91-
(8.1)
D A I KI
Figure 42.
Illustration of the force on an active grain.
-92-
For harder wheels with more bonding agent, the forces at the bond
bridges are distributed over a larger area and therefore the stresses are
lower.
With the bond bridges between the grains approximated as penny-
shaped slugs of constant thickness, the stresses would vary inversely
with the fraction of bonding agent in the wheel, Vb.
The tensile stress
in equation 8.1 can thus be written as
K
t
where K and
Vb)
are constants.
(8.2)
The expression within the parenthesis is
called the "bond stress factor".
For each contact between an active grain and the workpiece, there
is a probability PB that a bond fracture will occur.
is proportional
The total wear W
to the product of the probability of bond fracture PB
and the number of contacts N between the active grains and the workpiece.
N is proportional
to the number of grains n that are "instantaneously"
in contact with the workpiece.
Therefore the wear per active grain w
is given as
w
Experimentally,
=
OaCpB
(8.4)
Experimentally,
the
value
of n is obtained by multiplying the
the value of n is obtained by multiplying the
number of active grains per square inch (Tables 5, 6, and 7) by the
apparent area of contact aA between the wheel and the workpiece.
The
values of fH and fV can then be obtained by dividing FH and FV by n.
In view of the above, the wear rate per active grain w should
depend in some yet undetermined way on the bond stress factor.
-93-
Indeed
when w is plotted against the bond stress factor
(with
= .20) a single
straight line (Figure 43) is obtained on a semilogarithmic
equation 8.4 is taken as the wear in 20 passes.)
probabilities are also given.
for the steady state wear.
plot.
(W in
The corresponding
The data points in this figure are only
The wear rate per active grain is given by
thpfnrmla
_
w
=
.27 exp.
(8.5)
and the probability of bond fracture is given by
A]
-6
PB
The constants
=
3.32 x 10
exp
(8.6)
.27 and .51 in equation 8.5 were determined by the methods
of least squares with the bond stress factor taken as the error free
variable.
According
to equations 8.2, 8.5, and 8.6, the probability of bond
fracture and hence the wear rate is found to depend exponentially on
the tensile stress in the bond bridge.
was suggested by Yoshikawa
( 23
This same type of dependence
' 24) who considered the bond fracture from
the standpoint of static fatigue where the rate of fracture is expressed
by the Arhennius equation.
Although it is questionable whether the
fracture occurs in this way, the analysis does give an equation which
is consistent with the experimental observations.
The total wear observed after 100 passes
(Figures 35-37) requires
that only about one in twenty of the active grains experience a bond
fracture.
It would therefore be expected that most of the grains initially
-94-
I
m
I U.u
I1x04
0
50
5X10- 5
3
z
lc
C
-0
CD
r
2.0
2X1 0 - 5
-<
cL
n1~
1.0
xIx-5
I XIO
C()
z
Z
.5
0C
Ix0
-6
mo
':
--
LL
3:
C
.2
2X104
c2X-
I
1
"O
2
BOND STRESS
Figure 42.
3
FACTOR
4
5
fH-.)20fv
Correlation between the wear per active grain and the
bond stress factor.
-95-
'w
active would persist for the duration of the test.
Furthermore, since
the radial wear is only a small fraction of a grain dimension very few
"new" active grains would appear.
Therefore, it is to be expected that
the number of active grains in the wheel surface remain relatively
unchanged as grinding proceeds.
This was found to be true (Figure 15).
The particle size distributions
(Figures 38-40) indicate that a
small percentage of the total wear consists of attritious wear particles.
A rough estimate of this percentage can be made as follows.
For this
example, the results for the I-grade wheel with the fine dress and the
1018 steel workpiece
are used.
The average wear flat area over 100 passes (Figure 11) is about
3.5%.
The total area of the wheel which grinds is equal to the wheel
circumference
(
D
=
25.12 in.) times the width of the workpiece
(b = .25)
or 6.28 in. , and the total area of the wear flats is 3.5% of this or
.22 in.
2
The radial wheel wear after 100 passes has been measured to
be .0006 in. and therefore, the total volume of attritious wear is
(.0006) x (.22) or 1.22 x 10
aluminum oxide (p
Multiplying by the density of
.56 x 105 mg./in. 3 ) the attritious wear in 100
passes is about 6.8 milligrams.
wear
in.3 .
Comparing this to the accumulated
(Figure 35), the attritious wear constitutes about 10 per cent
of total wear.
This is more than would be expected from the particle size
distributions
(Figure 38) where attritious wear particles would be
expected to be smaller than 325 mesh.
wear debris is not recovered.
Undoubtedly
However,
some of the attritious
this does not change the previous
conclusion that most of the wear is due to grain and bond fracture.
-95a-
IX.
CONCLUSIONS
In this section the important conclusions of this investigation
are presented.
1.
The wear flat area on the face of the wheel uniquely determines
the grinding force components for a particular workpiece material and
for given grinding conditions.
Both the horizontal and vertical force
components increase linearly with the wear flat area.
(For steels this
is true only up to a critical wear flat area where burning occurs.)
This linear variation between grinding force and wear flat area is explained by considering
the force as the sum of a cutting force, due to
chip formation and a sliding force due to rubbing between the wear flats
and the workpiece.
2.
The specific cutting energy required in grinding increases linearly
with the melting temperature of the workpiece.
wear flat pressure is also higher
for
In most cases, the average
materials which require a larger
specific cutting energy.
3.
Grinding burn with steel occurs at a critical wear flat area which
depends on the particular steel being ground.
For all the steels, burn-
ing occurs at the same total grinding energy.
4.
Finer dressing results in a larger initial wear flat area on the wheel
and a greater tendency toward workpiece burn.
On the other hand, with
finer dressing a better surface finish is obtained.
For a particular grind-
ing operation, these two opposing factors must be carefully considered.
-96-
5.
Most of the grinding wheel wear is due to grain and bond fracture.
The rate at which the fracture wear occurs i
directly related to the
grinding forces.
6.
With harder wheels, smaller particles are produced since with their
stronger bonds, there is a greater probability of fracturing within the
grain than at the bond.
This is also related to the fact that harder
wheels have more active grains, larger wear flat areas, and hence require
larger grinding forces.
7.
Attritious wear particles constitute
of the total grinding wheel wear.
tious wear is the most important
an almost insignificant portion
However, in finish grinding, the attritype of wear as it is directly related
to the size of the wear flats, grinding forces, and workpiece burn.
The
abrasive best-suited for a particular workpiece should have both a low
attritious wear rate and a low rubbing friction coefficient.
8.
Virtually all the sliding energy and about 60 per cent of the cutting
energy are conducted to the workpiece as heat.
thermal expansion of the workpiece
flat area.
This is accomplished
dressing technique.
Grinding errors due to
can be minimized by reducing the wear
using either a softer wheel or a coarser
For instance, at 3.5% wear flat area with 1018 steel
(Figure 16), the thermal expansion for ten grinding passes is about .0007 inch.
At, 1.0% wear flat area, the thermal expansion is
proportionally
reduced by about 50%.
A
greater decrease in thermal expansion is obtained for material
which have a higher ratio of sliding energy flux, qF, to specific cutting
-97-
energy, uc.
9.
Peak grinding temperatures, which occur at the shear plane of
the chip, approach (or even exceed) the melting temperature of the
workpiece.
Over the whole wear flat, surface temperatures on the
order of 1100°F are obtained for mild steel.
I
-98-
X.
-SUGGESTIONS FOR FUTURE WORK
1.
The study of the relationship between the wear flat area and
grinding force should be extended to other conditions of speed and
feed.
For such an investigation
it would be desirable to use a
grinding machine and wheels which have high speed capabilities of
up to 10,000 R.P.M.
This should shed light on the dynamic effects
in the contact between
be interesting
the grain and the workpiece.
It will also
to observe if and in what manner the specific cutting
energy varies with the geometry and rate of chip formation.
2.
In finish grinding, the abrasive best suited for a particular
workpiece
should have a low attritious wear rate and low rubbing
friction coefficient.
Therefore,
it would be desirable to study
the sliding friction and wpar of abrasive materials against workpiece materials under simulated grinding
and temperature.
conditions of load, speed,
This should provide a rational basis of abrasive
selection for finish grinding.
3.
The grinding forces can be considered as the sum of cutting and
sliding components.
It would be desirable to study the action of
ing fluids in this light.
grind-
The possible lubrication effects of these
fluids could be clearly observed.
4.
ditions.
Fracture wear studies should be continued for other grinding conIn the long run, it might be possible to obtain a generalized
expression (analogous to equation 8.5) which will predict the wheel wear
as a function of grinding forces, wheelspeed,
_99-
grain size, bond material,
etc.
This should be particularly applicable to abrasive,machining
(bulk metal removal) where abrasive costs constitute a large portion
of the total expense.
1 no
REFERENCES
1.
G.I. Alden, "Operation of Grinding Wheels in Machine Grinding", Trans.
A.S.M.E., 1914, pp. 451-460
2.
R. Woxen, "Wheel-Wear in Cylindrical Grinding",
Akademien Handlingar, Nr. 124, 1933
3.
E. Rabinowicz, Friction and Wear of Materials, John Wiley and Sons, Inc.,
1965
4.
L.P. Tarasov, "Grindability
1174
5.
W.R. Backer, M.E. Merchant, "On the Basic Mechanics of the Grinding Process, Trans. A.S.M.E., Vol, 80 (1958), pp. 141-148
6.
J. Peklenik, "Beitrag zu Grundlagen des Scheifens", Doctoral Dissertation,
Ingeniors Vetenskaps
of Tool Steels, Trans A.S.M., 1951, pp. 1144-
Aachen Technische Hockschule, 1957
7.
J. Peklenik, "Untersuchen Uber Das Verschleisskriterium Beim Schleifen!',
Industrie-Anzeiger, Vol. 80 (1958), No. 19, pp. 280-284
8.
H. Yoshikawa, "Criterion of Grinding Wheel Tool Life", Bull. Japan
Society of Grinding Engineers, Vol. 3 (1963), pp. 29-32
9.
H. Yoshikawa, "Theory of Tool Life for Grinding Wheel", Paper Presented
at 15th Annual Meeting, C.I.R.P., Liege, Belgium, August 1965
10.
H.H. Tsuwa, "On the Behaviors of Abrasive Grains in Grinding Process"
Bull. Japan Society of Grinding Engineers, Vol. 1 (1961), pp.7 -8
11.
H. Tsuwa, "An Investigation of Grinding Wheel Cutting Edges", Trans.
A.S.M.E., Series B., Vol. 86, Nov. 1964, p. 371
12.
H. Tsuwa and S. Kawamura, "On the Wear by Attrition of Abrasive". Bull.
Society of Precision Engineering, Vol. 2, No. 1, 1966
13.
Y. Tanaka, H. Tsuwa, S. Kawamura, "Effect of Grinding Conditions on the
Journal of Japan Soc. of Precision
Performance of Grinding Wheels",
Engineering, Vol. 31 (1965), No. 3 (Translated by K. Nakayama)
14.
R.S. Hahn, "Technical Factors in the Operation of Grinding Machines",
A.S.T.M.E., Paper No. MR 67-592, (1967)
-101-
PAGES (S) MISSING FROM ORIGINAL
PAGE 102 MISSING
29.
G.S. Reichenbach, J.E. Mayer, S. Kalpakcioglu, and M.C. Shaw, "The
Role of Chip Thickness in Grinding",
Trans. A.S.M.E., Vol. 78
(1956), p. 847
30.
R.W. Story, "Forces and Force Ratios in Grinding with Coated Abrasives",
A.S.M.E. Paper No. 67-WA/Prod
-13
31,
K. Okushima, K. Hitomi, "Progress of Flank Wear and Variation of Tool
Forces", Bull. Japan Society of Precision Engineering, Vol. 1.,No. 2.
1965, p. 6 9
32.
E.G. Thomsen, A.G. Mac Donald, S. Kobayashi, "Flank Friction Studies
with Carbide Tools Reveal Sublayer Plastic Flow", Trans. A.S.M.E.,
Vol. 84 B, 1963, p.53
33.
G.F. Micheletti, A. De Fillippi, R. Ippolito, "Tool Wear and Cutting
Forces in Steel Turning, CIRP International Conference on Manufacturing
Technology, 1967, p. 513
34.
N.N. Zorev, "Mechanics of Contact on the Clearance Surface", Chapter 3,
pp. 129-180, in Metal Cutting Mechanics, Translated from Russian,
Published by Pergamon Press, 1966
35.
L.A. Galin, Contact Problems in the Theory of Elasticity, Translated
from Russian,Published
by North Carolina State College, School of
Sciences and Applied Mathematics, Oct. 1961
36.
H. Opitz, W. Ernst, K.F. Meyer, "Grinding at High Cutting Speeds",
Proc. of 6th International M.T.D.R. Conference, September 13-15,
1965, pp. 581-595
37.
W.E. Littman, The Influence of the Grinding Process on the Structure of
Hardened Steel, Sc. D. Thesis, M.I.T, November 1953. Most of this is
also published under the same title by W.E. Littman and J. Wulff, Trans;.
A.S.M., Vol. 47, 1955, pp. 692-714
38.
L.P. Tarasov, "Some Metallurgical Aspects of Grinding", Machining-Theory.
and Practice, A.S.M., 1950, pp. 409-464
39.
J.O. Outwater, M.C. Shaw, "Surface Temperatures
A.S.M.E., Jan. 1952, pp. 73-86
40.
J.C. Jaeger, "Moving Sources of Heat and the Temperature at Sliding
Contacts", Proc. Royal Society of New South Wales, Vol. 76, (1942),
pp. 203-224
-103-
in Grinding", Trans.
41.
K. Sato, "Grinding Temperature", Bull. Japan Society of Grinding
Vol. 1 (1961), pp. 31-33
Engineers,
42.
R.H. Brown, "Forces in Single Grit Grinding", M.S. Thesis, M.I.T.,
August 1957
43.
See K. Sato, "Progress of Researches on Grinding Mechanics in
Japan", Bull. Japan Society of Grinding Engineers, Vol. 5
(1965), pp. 1-25
44.
C.J. Smithells, Metals Reference Book, Vol. II, 3rd Edition, 1962
45.
T. Orioka, "Probabilistic Treatment on the Grinding Geometry",
Bull. Japan Society of Grinding Engineers, Vol. 1 (1961), pp. 27 - 29
46.
K. Nakayama, M.C. Shaw, "An Analytical Study of the Finish Produced
in Surface Grinding", Unpublished
-104-
APPENDIX A
CALCULATION OF THE MAXIMUM NUMBER OF ACTIVE GRAINS
The maximum number of active grains per square inch in the wheel
surface is assumed to be identical to the number of grains which intersect one square inch of a plane which passes through the grinding wheel.
For simplicity,
the packing of grains is assumed to be cubic, with the
center of each grain located at a point where four cubes meet.
The plane
in question is assumed to contain a square array of grains.
For a wheel with the densest possible packing, the grain spacing is
equal to the mean grain diameter.
For such a wheel, the per cent of grain
has been experimentally determined
to be 58 per cent for the 32 A46 abra-
sive.
This was accomplished by tightly packing abrasive grains into a
known volume and comparing their weight to the weight which would result
if the volume were 100% aluminum oxide. The wheels used here are 48 per
cent abrasive.
Their mean grain spacing is therefore equal to the cube
root of 58/48 times the mean grain diameter or .018 inches.
number of active grains per square inch is then 1/(.018)
2 .
grains/inch
- 105-
2
The maximum
or 3240
APPENDIX B
CALCULATION OF TEMPERATURE
DUE TO CUTTING
The cutting temperature is calculated as moving band source of
width equal to (t2 )50 as given by equation 6.7.
is a rectangular source of dimensions
More precisely this
(t2)50 by 1/2 r (tl)max but the
(40)
band source solution provides a good approximation
The total cutting energy is
FHC V
-
(1.333)(6250) 12
1666 in. lb
of which the fraction R1 is
(B.1)
sec.
'C60
conducted to the workpiece.
Since the
cross sectional area of the chip at 50 per cent of the cut is
also
the average chip cross sectional area, the source strength qc which is
the energy flux into the workpiece
A C[t)
a
2 50
given by
3 22 x 108 in. lb.
(.61)(1666
R1 FHC V
qc-
i
x r x (t )
2
max
I-
(.09)(6000)(2.34)10
-8 -3.22 x 10
in.
(B.2)
For moving heat source calculations,
the value of the nondimensional
L =
necessary to calculate
variable L which is defined as
V1
(B.3)
where
1 - half width of band
V
it is
velocity of the source
- thermal diffusivity
-106-
2
sec.
In this case
= 9.4 x 10- 3 in. 2 /sec
1
(tl)max
=
62.5 x 10- 6 in.
4
V = 6250 ft./min = 1250 in
sec.
=
and therefore
L = (1250)(62.5 x 106)
(2)(9.4 x 10
3
The temperature distribution
=
415
)
(B.4)
on the surface is obtained as a function of
the non-dimensional variable X,
(B.5)
2Ck
X
where x is the local variable in the plane of the source measured from
the center of the band in the direction of the velocity V.
The temperature distribution is given by the function
2qc c
T
c
=
c
'rkV
[ I(X + L) - I (X-L)]
where k is the thermal conductivity
(B.6)
(k = 4.10 lb./sec.°F) and I(X+L) and
I(X-L) are integrals which cannot be explicitly evaluated and are given
in tabular form in reference
(40).
Equation B.6 then becomes
-8
= (2)(3.22 x 10
T
c
-3
)(9.4 x 103)
[I(4.15 x X) - I(4.14 -X)]
() (4.10)(1250)
Table B.1 gives the values of T
as a function of X.
(B.7)
With the appropriate
shift in the variable x, this result is plotted in Figure 33 as curve (a).
-107-
APPENDIX
C
CALCULATION OF TEMPERATURES
Essentially
the temperature T
the same procedure
DUE TO SLIDING
as in Appendix B is used to calculate
due tofsliding between the wear flat and the workpiece.
The source strength or energy flux to the surface is given by R 2 times qf
In this case R2 is approximately unity and
where qf is given in Table 14.
qf is 2.28 x 106 in.lb./(in.2 sec.).
The other parameters of interest are
OV=
.
V = 1250 in./sec.
1 = (.004)/2 = .002 in.
= 9.4 x 10 - 6 in.2/sec.
and
k = 4.10 lb./(sec.
The nondimensional
L
=
F).
parameter L is then given by
(1250)(2 x 10-3)
133
(C1)
3 )
(2)(9.4)(10
For such a large value of L, the temperature
distribution under the band
(-L X L) is approximated by
T = 2/
(C.2)
2(L-X)
The maximum temperature rise (TS)max
occurs at the trailing edge of the
band and is equal to
2qf a
(TS max
kV
(2)(2.28 x 10 6)(9.4 x 10- 3 )( 27)
2
=
()
- 110F
(4.10) (1250)
(C.3)
-108-
and the average temperature rise within the band (Ts)ave
is two-thirds
of the maximum or
T )
=
(Ts)ave
3
(T )
s max
=
740 F.
(C.4)
With the appropriate shift of the coordinate x, the temperature distribution
in equation C.2 is presented as curve (b) in Figure 33.
-109-
APPENDIX
CALCULATION
D
OF THE AVERAGE TEMPERATURE
IN
THE GRINDING
AREA
The heat source is taken as a band of width 1c, the undeformed
length, with a velocity
equal to the table speed v.
chip
The grinding energy
input rate Q is given by
Q
FHV
(D.1)
where FH is taken at A
is
3.5% from Figure 16, and the total energy flux q
=
equal to Q divided the apparent area of contact A a.
Q_ =
q
3.42 x 103
a
= 1.52 x10
10
5
in.lb.
.0225
in.
The fraction of this energy conducted to the workpiece
Figure 31 where R at A = 3.5% is approximately
The value of the nondimensional
(8 x
1
L
-
23
12
-
(D.2)
sec.
is obtained from
.80.
variable L is then
1
)(.009 x -)(.3)
2
860
= 3.8
(D.3)
2(9.4 x 10 -3 )
For this value of L, from reference (40), the maximum value of the temperature in the band is equal to
(6.3) (2)Rqg
max
kv
(T.)
(6.3)(2)(.80)(1.52 x 105)(9.4 x 10(X) (4.10) (8 x 60 )
721F
(D.4)
and the average value over the band is
(T
A)
A ave
=e
(4.7)(2)Rq( = 538F.
nkv
-110-
Table 1.
)escription of Wheels
Wheel
Grain
Grain
Designation
Type
Size
Per Cent
32A461G8VG
32 A
46
3.1
48
32A461H8VG
32 A
46
4.4
48
32A4618tVG
32 A
46
5.8
48
32A461J8VG
32 A
46
7.2
48
32A461K8VG
32 A
46
8.6
48
-111-
Bond Weight
Grain Volume
Per Cent
Table 2.
Workpiece Materials
Material
Nominal Composition, %
SAE 1018 Steel
.18C, .25 Mn, Bal Fe
89 B
AlSl 52100 Steel
1.00C, .35 Mn, .30 Si, 1.40 Cr, Bal Fe
62 C
T1 High Speed Steel
0.7C, 18W, 4Cr,
64 C
Molybdenum
100 Mo
95 B
.130A Titanium
92 Ti, 8 Mn
33 C
Niobium
100 Nb
95 B
Stellite No. 6B
3.00* ni, 2.00* Si, 3.00* Fe
38 C
V, Bal Fe
2.00* Mn, 30 Cr, 1.50 Mo,
4.25 W, 1.25 C, Bal. Co
* Maximum
-112-
Rockwell Hardness
Table 3.
Wheel Dressing - Experimental Results
Wheel
Designation
Dress
Active
Grains/in.
Wear Flat
Area, A,%
Per Cent
Bond Fracture
coarse
fine
424
476
.50
32A461H8VBE
coarse
fine
567
592
.97
1.06
59.2
32A46118VBE
coarse
fine
669
849
1.20
1.48
50.2
32A461J8VBE
coarse
fine
939
1132
1.67
1.85
43.8
32A461K8VBE
coarse
fine
1145
1235
2.04
2.32
39.6
32A46lG8VBE
-113-
70.4
.55
Table 4.
Sieve Number - Screen
Sieve Number
Screen
enin
Opening, in.
20
.0331
40
.0165
60
.0098
80
.0070
100
.0059
200
.0029
325
.0017
-114-
Table 5.
Forces and Wear Flats - 1018 Steel, Fine Dress
( V = 6250 ft./min.,
Active Wear Flat
Grains
Area
Wheel
Passes
per in
A,
v
-H'-
8 ft./min.,
Wear Flat
Arel/Grain6
in.
x 10
d = .001 in.)
Horizontal Vertical
Force
Force
_FH lbs.
Fv, lbs.
FH/Fv
-
1.13
1.23
1.50
21.1
17.3
25.8
23.9
29.2
1.37
1.19
1.99
1.41
1.71
23.7
21.0
30.9
24.8
26.6
1.89
1.81
1.84
2.04
1.96
2.39
2.21
2.30
2.43
2.70
.79
.82
1119
1132
1119
1132
1106
1122
2.80
3.43
3.84
4.77
5.30
25.2
30.2
34.2
42.1
47.9
2.49
.80
.79
3.07
4.07
6.35
3.12
3.43
4.49
9.42
22.85
20
*40
*
60
*80
* 100
926
1350
1106
1222
1363
Ave. 1193
3.31
5.32
5.60
6.80
6.02
35.7
39.4
50.7
55.4
44.2
3.12
4.66
7.30
7.25
7.97
4.83
8.88
29.25
31.45
34.95
.64
20
40
60
80
* 100
5.97
6.27
6.62
7.31
7.55
44.3
47.5
51.8
47.9
55.4
6.50
7.80
8.04
8.94
8.25
18.78
31.95
34.20
38.40
36.75
32A461G8VG
32A461H8VG
20
40
60
80
100
Ave.
270
424
437
514
514
432
20
40
60
80
100
578
566
643
566
643
Ave.
32A461I8VG
32A461J8VG
20
40
60
*
80
* 100
Ave.
32A461K8VG *
*
*
*
*
.57
.73
1.64
1.56
1.56
1.63
1.66
2.02
2.03
1.85
1.91
1.96
.81
.77
.84
.85
.85
.80
.84
.73
Z'60
1350
1325
1273
1530
1363
Ave. 1368
Workpiece Burned
-115-
2'.69
.68
.43
.28
.52
.25
.23
.23
.35
.24
.24
.23
.22
Forces and Wear Flats - 1018 Steel, Coarse Dress
Table 6.
v = 8 ft./min.,
(V = 6250 ft./min.,
Active Wear Flat
Area
Grains
Wheel
32A4618VG
Passes
H/Fv
.66
1.55
1.57
1.60
1.51
1.56
.93
604
630
668
60
630
80
669
100
Ave. 640
1.04
1.48
1.81
1 81
2.00
17.3
23.4
27.0
28.8
29.9
2.00
2.04
2.12
2.20
2.31
2.45
2.49
2.74
2.87
3.11
.82
.82
.77
.77
.74
682
669
720
707
759
Ave. 707
1.20
1.57
1.53
1.94
1.90
17.6
23.4
21.2
27.4
25.2
1.96
2.00
2.09
2.19
2.40
2.06
2.30
2.43
2.75
3.26
.94
952
862
862
862
1.67
1.85
2.41
2.63
2.59
17.6
21.6
28.1
30.6
27.0
2.02
2.06
2.06
2.49
2.40
2.25
2.23
2.34
3.04
3.00
.90
2.91
2.96
3.28
4.12
4.16
23.0
24.8
28.1
35.3
36.0
2.13
2.21
2.36
2.72
4.47
2.34
2.64
3.15
4.02
12.26
.91
.84
100
398
360
347
386
334
Ave. 365
.44
.56
20
40
20
40
60
80
100
32A461J8VG
in. 2 x 10
1.33
1.36
1.38
1.36
1.45
60
80
32A46118VG
A,%
Vertical
Horizontal
Force
Force
_Fv, lbs.
F , lbs
)
11.2
15.5
14.0
11.5
19,8
20
40
32A461H8VG
per in.
Wear Flat
Area/Grai~
d = .001 in.
20
40
60
80
966
100
.49
.44
.86
.87
.87
.86
.86
.86
.80
.74
.92
.88
.82
.80
Ave. 900
32A461K8VG
1273
1183
1170
1170
* 100
1157
Ave. 1190
20
40
60
80
* Workpiece burned
-116-
.75
.68
.36
Table
7,
Forces and Wear Flats - 52100 Steel, Fine Dress
(V = 6250 ft./min.,
Active Wear Flat
Grains
Wheel
32A461G8VG
Passes
per in2
20
40
60
80
100
399
424
463
399
437
424
32A461K8VG
*
H orizontal Vertical
Force
Force
Area/Grain
in.2 x 10-6
FH, lbs. _FV, lbs.
FH/FV
V
.88
3.25
3.45
3.77
3.98
4.09
.46
.44
.43
.42
.42
579
630
669
656
720
651
.69
.97
1.11
1.48
1.67
11.9
15.4
16.6
22.6
23.2
1.95
2.04
2.56
2.31
2.51
4.74
4.91
5.21
5.92
6.72
.41
.42
.44
.39
.37
836
836
797
784
887
841
1.34
1.71
1.90
1.76
1.71
16.0
20.5
.23.8
22.4
19.3
2.11
2.34
2.13
2.23
2.36
4.72
5.06
5.47
5.96
6.79
.45
.46
20
40
60
80
*100
1067
1080
1106
1042
1119
Ave. 1095
1.99
2.11
2.17
2.26
2.57
3.34
4.72
5.13
5.66
7.66
12.75
.45
.42
2.55
2.78
3.05
18.7
18.9
23.1
26.7
27.3
20
40
60
* 80
*100
1.44
1.76
2.69
3.29
3.80
13.0
15.9
25.9
28.1
34,4
2.43
2.43
2.70
4.19
4.87
6.34
22.64
24.34
.57
20
40
60
80
100
20
40
60
80
100
Ave.
32A461J8VG
A %
Wear Flat
1.51
1.53
1.62
1.67
1.70
Ave.
32A461I8VG
...
Area-
d = .001 in.)
12.3
13.7
17.5
19.0
20.1
Ave.
32A461H8VG
8 ft./min.,
v
1106
1119
1080
1170
1106
Ave. 1116
.49
.58
.81
.76
2.04
Workpiece burned
-117-
5.,28
5.45
.39
.37
.35
.40
.34
.26
.50
.43
,23
.22
Forces and Wear Flats - T1 Steel, Fine Dress
Table 8.
(V = 6250 ft./min.,
v
Wear Flat
Passes
Wheel Designation
8 ft./min.
d = .001 in. )
Horizontal
Force, F,
lbs.
Vertical
Force, F , lbs.
V ~
32A461G8VG
10
20
30
40
50
.72
.90
.95
1.06
1.20
1.83
2.00
2.04
2.09
2.09
6.54
6.92
8.08
8.68
8.68
32A461H8VG
10
20
30
40
50
1.44
1.71
1.91
2.22
2.08
2.35
2.43
2.70
2.83
3.04
8.85
9.62
11.92
13.46
15.38
*
10
*
20
30
40
50
1.99
2.36
2.36
2.59
2.78
2.83
3.04
3.48
5.00
5.43
10.38
12.31
18.46
26.92
34.61
*
*
32A461J8VG
*
*
*
*
=
Workpiece burned
-118-
Table 9.
Forces and Wear Flats - 130 A Titanium, Fine Dress
( V= 6250 ft./min,
Wheel Designation
32A461G8VG
32A461H8VG
Passes
Wear
F].at
Area,
AL,
d =
)01
.C*
in.
Horizontal
Force
FH ; bs.
-zH
Vertical
Force F
lbs.
10.19
8.68
7.74
7.55
7.55
10
20
30
40
50
1.48
1.48
1.16
.88
.97
2.77
2.77
2.55
2.34
2.21
10
20
30
40
4.03
3.52
3.66
3.80
3.98
6.38
5.53
5.96
5.98
6.17
13.21
12.45
13.58
12.45
13.21
4.40
4.31
5.51
4.54
5.53
5.74
5.53
5.50
11.32
12.83
14.15
13.58
50
32A461J8VG
v = 8 ft./min.,
10
20
30
40
-119-
Table 10.
Forces and Wear Flats - Niobium, Fine Dress
(V
Wheel Designation
32A461G8VG
6250 ft./min.,
Horizontal
Passes
Area, A, %
Force,
10
1.02
1.27
1.20
3.62
4.47
3.91
A.91
3.24
3.61
3.33
7.87
8.72
8.09
12.07
13.96
12.83
30
4.86
5.19
5.05
9.36
9.79
10.21
17.36
19.62
20.38
10
20
5.42
6.53
11.49
12.77
14.62
23.40
10
20
30
32A4611I8VG
32A461K8VG
Vertical
Wear Flat
20
40
32A461H8VG
d = .001 in.)
v = 8 ft./min.,
10
20
-120-
, lbs.
Force, F,
5.85
5.47
lbs.
Table 11.
Forces and Wear Flats - Molybdenum/
(V = 6250 ft./min.,
Wheel Designation
32A461G8VG
Passes
Wear Flat
Area, A,
d = .001 in.)
Horizontal
Vertical
Force, FH, lbs.
Force, F,
6.04
5.28
4,53
3.77
40
.31
10
3.28
3.82
4.07
3.84
11.49
12.77
13.19
13.62
20.38
22.64
22.64
22.64
4.35
5.79
6.29
6,29
15.32
16.17
18.72
18.72
24.15
27.36
32.08
32.08
20
30
40
32A46iK8VG
8 ft./min.,
3.83
3.83
2.98
2.77
.86
.46
10
20
30
32A461H8VG
v
Fine Dress
10
20
30
.40
.65
-121-
lbs.
Forces and Wear Flats - Stellite No. 6B, Fine Dress
Table 12.
(V = 6250 ft./min.,
v = 8 ft./min.,
Wear Flat
Wheel Designation
Passes
Area, A,%
d = .001 in.
Horizontal
Force, FH, lbs.
)
Vertical
Force, FV, lbs.
32A461G8VG
10
20
30
40
50
1.57
1.57
1.67
1.20
1.39
2.68
3.19
3.62
3.70
3.53
9.43
11.32
14.34
15.47
15.09
32A461H8VG
10
1.57
2.04
2.31
2.64
2.54
3.83
4.26
4.89
5.53
5.74
13.58
17.36
20.38
27.34
28.30
2;64
3.10
3.01
3.19
3.29
5.32
5.96
6.38
6.81
7.23
25.47
30.19
32.08
33.96
36.79
3.06
3.52
3.56
3.56
4.07
6.38
6.60
7.66
7.66
7.87
32.08
33.96
39.62
42.45
43.40
20
30
40
50
32A461J8VG
10
20
30
40
50
32A461K8VG
10
20
30
40
50
-122-
Table 13.
Forces and Wear Flats (V = 3125 ft./min.,
Passes
Wheel Deisgnation
32A461G8VG
32A461H8VG
32A461I8VG
=
4 ft./min.,
Wear Flat
Area, A, %
d = .001 in.)
Horizontal
bs. e FH
la.
1.87
1.74
1.70
1.83
1,79
20
40
60
80
100
.42
.63
20
40
60
80
100
1.20
20
2.64
2.87
3.43
3.80
4.21
3.83
4.68
4.26
*
*
40
60
80
*
100
.46
.44
.44
1.57
1.39
1.85
1.76
*
*
60
80
2.92
4.21
4.77
4.63
*
100
5.37
32A461K8VG
20
40
*
v
1018 Steel, Fine Dress
Workpiece burn
-123-
2.55
2.47
2.55
2.64
2.94
4.89
5.74
7.02
6.80
8.09
8.94
8.30
Vertical
Force, FV
2.57
2.34
2.26
2.38
2.42
3.02
2.83
2.94
3.21
3.28
5.09
6.04
8.30
11.32
15.85
5.28
10.56
18.11
23.40
23.58
lbs.
*,4 %O
0
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(IN
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Co
.4.
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D
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ru
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co
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-.
N
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A~~~~~~~-**
-4
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S
r.
02
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10
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0
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00
co r-
la.
o0
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c +
L +
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W
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-TN
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400
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C, +l
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;I
'4.
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C,
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-T
rUf
Cl\
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cr
Q
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a:
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0
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0O
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W
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'-4i
.M
Ca
--'4
>
44
Co
O
CO
C
'.0
11
Nr
'.0
Sf
N\
'.0
Sf
N)
'.0
O
1t
N)
0
0%
,-4
0
,
C
COC
Oq
N
'.0
Ni
'.0
Sf
N
'0
r-q
4'
r-I
0
Sf
NI
0
O
0
0
O
0
Sf
'.0
Sf
N
'0
r
10
0D
Sf
N
N
'.0
(4
e
cN
(
-4
,-4
-
IU
3
U
00
co
O--
,-4
I::
'4)
0
N
O
c~4
·
U,
N
I
¢
i
A
i,,-4
,
-4 ong
4c
O -'U,
,r-
v
4
,,
c)
CO
V4
~r-44l
D.
Co
*
0
-
CvO
0CP
-
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4Y
-124-
O
4
O
Table 15,
Energy Partition - 1018 Steel, Fine Dress
(V = 6250 ft./min.,
Wheel Designation
v = 8 ft./min., d = .001 in.)
Wear Flat Area, A,%
Energy to Workpiece,R
32A461G8VG
.74
.64
32A461H8VG
1.34
.69
2.82
.75
3.06
.76
3.98
.81
32A461K8VG
-125-
Table 16.
Steel
Surface, itntsh 1018&
(V = 6250 ft./min.,
Wheel Designation
32A461G8VG
Passes
v
8 ft./min.,
Fine Dress
20
40
100
15
17
14
12
15
60
80
32A461H8VG
32A461I8VG
28 microinches
28
30
31
30
20
12
26
13
26
60
80
13
100
13
27
24
24
20
12
14
13
25
35
27
26
25
25
25
10
25
30
30
35
23
23
20
25
30
30
30
20
22
22
22
14
60
80
100
20
40
60
80
100
32A461K8VG
microinches
Coarse Dress
40
40
32A461J8VG
d - .001 in.)
20
40
60
80
100
-126-
24
22
22
40
Table 17.
Fine Dress
Wheel Wear - 1018 Steel,
~~~~~~~~~~~~~~~I
H ~
i
_
!
11
Jl,
v = 8 ft./min.,
( V = 6250 ft./min.,
d =
.001 in.)
Accumulated Wear, Mg.
Wheel Designation
Passes
32A461G8VG
20
40
60
80
100
85.0
33.0
20.1
23.5
29.0
85.0
118.0
138.1
161.6
190.6
32A461H8VG
20
40
60
80
100
59.6
28.6
17.4
18.4
12.7
59.6
88.2
105.6
124.0
136.7
32A461I8VG
20
40
60
80
100
46.3
23.9
22.5
23.0
52.0
46.3
70.2
92.7
115.7
167.7
32A461J8VG
20
40
80
100
46.0
35.0
39.8
41.2
40.3
46.0
81.0
120.8
162.0
202.3
20
40
60
80
100
61.6
33.6
35.2
28.4
26.0
61.6
95.2
130.4
158.8
184.8
60
32A461K8VG
-127-
Wear, Mg.
Table 18.
Wheel Wear - 1018 Steel, Coarse Dress
( V= 6250 ft./min.,
Wheel Designation
Passes
32A461G8VG
20
v
=
8 ft./min.,
Wear, Mg.
40
60
80
100
32A461H8VG
20
40
60
80
100
32A461I8VG
20
40
60
80
100
32A461J8VG
20
40
60
80
100
32A461K8VG
20
40
60
80
100
-128-
d =
.001 in.)
Accumulated Wear, Mg.
83.3
30.6
28.0
16.7
17.4
83.3
113.9
158.6
158.6
176.0
39.0
16.6
12.0
14.8
13.9
39.0
55.6
67.6
82.4
96.3
29.0
11.1
10.4
11.3
8.4
29.0
40.1
50.5
61.8
70.2
30.1
14.4
11.6
11.8
10.0
30.1
44.5
56.1
67.9
77.9
29.5
21.9
16.5
11.2
19.1
29.5
51.4
67.9
78.9
98.0
Table 19.
( V
Wheel Wear - 52100 Steel, Fine Dress
6250 ft./min.,
Wheel Designation
v = 8 ft./min.,
Wear, Mg.
Passes
d = .001 in.)
Accumulated Wear, Mg.
32A461G8VG
20
40
60
80
100
30.0
15.6
11.3
10.9
13.4
30.0
45.6
56.9
67.8
81.2
32A461H8VG
20
40
60
80
100
29.2
10.1
8.6
8.7
8.8
29.2
39.3
47.9
56.6
65.4
32A461I8VG
20
40
60
80
100
25.7
12.6
9.8
9.1
7.2
25.7
38.3
48.1
57.2
64.4
32A461J8VG
20
40
60
80
100
23.4
31.1
39.4
46.6
58.5
23.4
31.1
39.4
46.6
58.5
32A461K8VG
20
40
60
80
100
20.7
4.7
5.8
9.5
12.1
20.7
25.4
31.2
40.7
52.8
-129-
Table B.1
Calculated Values of T
Vx
TC
C
L
O
m
376
.5L
1410
0
1940
.5L
2350
-L
2327
-2L
1367
-3L
1053
-3.5L
989
-5L
865
-10L
639
-20L
414
-30L
357
-50L
320
-80L
263
-130-
F
BIOGRAPHICAL NOTE
The author was born June 20, 1941 in Boston, Massachusetts.
lived in Malden, Massachusetts
He
until his graduation from the Malden
public schools in 1959.
In 1959, the author entered M.I.T. where he was awarded the
degrees of Bachelor of Science in Mechanical Engineering
and Master of Science in 1965.
of Liquid Lubricants
His master's
in 1963,
thesis entitled "Behavior
in Vacuum" was supervised by Dr. G. S. Reichenbach.
The author was elected to Pi Tau Sigma and Sigma Xi while
attending M.I.T.
The author was married to the former Judith Greenberg of Valley
Stream, New York on August 30, 1964.
-131-